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2 <p>Last updated on<strong>November 27, 2025</strong></p>

3 <p>The volume of the cylinder is the capacity of the material it holds. A cylinder is a three-dimensional shape that has a circular base. In this topic, we will learn more about the volume of cylinders with solved examples for better understanding.</p>

4 <h2>What is the Volume of Cylinder?</h2>

5 <p>The volume<a>of</a>the cylinder is the space it occupies. It can be calculated by using the<a>formula</a> </p>

6 <p>V = ℼr2h.</p>

7 <p>Here, r is the radius of the circular<a>base</a>.</p>

8 <p>h is the height of the cylinder.</p>

9 <p>ℼ is approximately 3.14159.</p>

10 <p>In real life, the cylinder volume is used in<a>geometry</a>, engineering, etc. </p>

11 <h2>Volume of Cylinder Formula</h2>

12 <p>We use the following ways to find the volume of the cylinder. </p>

13 <ol><li>Volume of cylinder with height and radius.</li>

14 <li>Volume of cylinder with height and diameter.</li>

15 <li>Volume of cylinder with slant height. </li>

16 </ol><h3>Volume of Cylinder With Height and Radius</h3>

17 <p>By substituting the values of height and radius of the given cylinder in the formula V = ℼr2h, we can find the volume of the cylinder. </p>

18 <p>Example: Find the volume of a cylinder with a radius 5 cm and height 10 cm.</p>

19 <p>Given, radius (r) = 5</p>

20 <p>Height (h) = 10</p>

21 <p>Using the formula, V = ℼr2h</p>

22 <p>V = 3.14159 × 52 × 10 </p>

23 <p>= 3.14159 × 25 × 10 </p>

24 <p>= 785.4 </p>

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27 <h3>Volume of Cylinder With Height and Diameter</h3>

26 <h3>Volume of Cylinder With Height and Diameter</h3>

28 <p>When the diameter of the cylinder is given instead of the radius, we need to change the formula to r = d/2.</p>

27 <p>When the diameter of the cylinder is given instead of the radius, we need to change the formula to r = d/2.</p>

29 <p>Therefore, the formula becomes V = ℼ(d/2)2h.</p>

28 <p>Therefore, the formula becomes V = ℼ(d/2)2h.</p>

30 <p>Let’s see this using a simple example, find the volume of a cylinder with a diameter 8 cm and height of 12 cm.</p>

29 <p>Let’s see this using a simple example, find the volume of a cylinder with a diameter 8 cm and height of 12 cm.</p>

31 <p>Here, diameter = 8 cm.</p>

30 <p>Here, diameter = 8 cm.</p>

32 <p>height = 12 cm.</p>

31 <p>height = 12 cm.</p>

33 <p>Using the formula, V = ℼ(d/2)2h</p>

32 <p>Using the formula, V = ℼ(d/2)2h</p>

34 <p>V = 3.14159 × (8/2)2 × 12 </p>

33 <p>V = 3.14159 × (8/2)2 × 12 </p>

35 <p>= 3.14159 × 42 × 12 </p>

34 <p>= 3.14159 × 42 × 12 </p>

36 <p>= 3.14159 × 16 × 12</p>

35 <p>= 3.14159 × 16 × 12</p>

37 <p>= 603.2 </p>

36 <p>= 603.2 </p>

38 <h3>Volume of Cylinder With Slant Height</h3>

37 <h3>Volume of Cylinder With Slant Height</h3>

39 <p>To find the volume of a cylinder with the slant height first, we need to find the height using the Pythagorean theorem, and then we use the formula, V = ℼr2h. </p>

38 <p>To find the volume of a cylinder with the slant height first, we need to find the height using the Pythagorean theorem, and then we use the formula, V = ℼr2h. </p>

40 <p>For example, find the cylinder volume with a slant height of 13 cm and a radius of 5cm.</p>

39 <p>For example, find the cylinder volume with a slant height of 13 cm and a radius of 5cm.</p>

41 <p>For finding the height using Pythagorean theorem, h = √l2 - r2</p>

40 <p>For finding the height using Pythagorean theorem, h = √l2 - r2</p>

42 <p>= √132 - 52</p>

41 <p>= √132 - 52</p>

43 <p>= √169 - 25</p>

42 <p>= √169 - 25</p>

44 <p>= √144</p>

43 <p>= √144</p>

45 <p>= 12</p>

44 <p>= 12</p>

46 <p>Now for finding the volume, V = ℼr2h</p>

45 <p>Now for finding the volume, V = ℼr2h</p>

47 <p>= 3.14159 × 52 × 12 </p>

46 <p>= 3.14159 × 52 × 12 </p>

48 <p>= 3.14159 × 25 × 12</p>

47 <p>= 3.14159 × 25 × 12</p>

49 <p>= 942.48 </p>

48 <p>= 942.48 </p>

50 <h2>How to Derive the Volume of Cylinder Formula?</h2>

49 <h2>How to Derive the Volume of Cylinder Formula?</h2>

51 <p>The volume of the cylinder formula was derived by clearly understanding how much space the cylinder occupies. The volume of the cylinder can be calculated by using the volume formula. The following step-by-step explanation allows kids to understand how the formula is derived.</p>

50 <p>The volume of the cylinder formula was derived by clearly understanding how much space the cylinder occupies. The volume of the cylinder can be calculated by using the volume formula. The following step-by-step explanation allows kids to understand how the formula is derived.</p>

52 <p><strong>Step 1:</strong>Understanding shape </p>

51 <p><strong>Step 1:</strong>Understanding shape </p>

53 <p>The cylinder is like a stack of many discs placed on the top of the other. The volume of the cylinder is multiplied by the total area of the base with the height (<a>number</a>of discs stacked). </p>

52 <p>The cylinder is like a stack of many discs placed on the top of the other. The volume of the cylinder is multiplied by the total area of the base with the height (<a>number</a>of discs stacked). </p>

54 <p><strong>Step 2:</strong>Find the area of the base</p>

53 <p><strong>Step 2:</strong>Find the area of the base</p>

55 <p>The base of a cylinder is circular. Therefore, the area of the circle is given as,</p>

54 <p>The base of a cylinder is circular. Therefore, the area of the circle is given as,</p>

56 <p>Area of base = ℼr2.</p>

55 <p>Area of base = ℼr2.</p>

57 <p><strong>Step 3:</strong>Multiplying the base with height</p>

56 <p><strong>Step 3:</strong>Multiplying the base with height</p>

58 <p>To get the total volume of cylinder, we need to multiply the area of base with height of the cylinder</p>

57 <p>To get the total volume of cylinder, we need to multiply the area of base with height of the cylinder</p>

59 <p>Volume = Area of Base × Height.</p>

58 <p>Volume = Area of Base × Height.</p>

60 <p>V = ℼr2 × h.</p>

59 <p>V = ℼr2 × h.</p>

61 <p><strong>Step 4:</strong>Final Formula</p>

60 <p><strong>Step 4:</strong>Final Formula</p>

62 <p>The final formula is written as:</p>

61 <p>The final formula is written as:</p>

63 <p>V = ℼr2h. </p>

62 <p>V = ℼr2h. </p>

64 <h2>How to Find the Volume of Cylinder?</h2>

63 <h2>How to Find the Volume of Cylinder?</h2>

65 <p>To find the volume of the cylinder, the following steps are used.</p>

64 <p>To find the volume of the cylinder, the following steps are used.</p>

66 <p><strong>Step 1:</strong>Understanding the formula</p>

65 <p><strong>Step 1:</strong>Understanding the formula</p>

67 <p>The volume of a cylinder is: V = ℼr2h.</p>

66 <p>The volume of a cylinder is: V = ℼr2h.</p>

68 <p>Here, V = volume of the cylinder</p>

67 <p>Here, V = volume of the cylinder</p>

69 <p>r = Radius of the base.</p>

68 <p>r = Radius of the base.</p>

70 <p>h = Height of the cylinder</p>

69 <p>h = Height of the cylinder</p>

71 <p>ℼ is approximately 3.14</p>

70 <p>ℼ is approximately 3.14</p>

72 <p><strong>Step 2:</strong>Measuring the height and radius of the cylinder</p>

71 <p><strong>Step 2:</strong>Measuring the height and radius of the cylinder</p>

73 <p>Measure the radius of the base and the height of the cylinder.</p>

72 <p>Measure the radius of the base and the height of the cylinder.</p>

74 <p><strong>Step 3:</strong>Use the formula</p>

73 <p><strong>Step 3:</strong>Use the formula</p>

75 <p>Apply the height and radius values and calculate, we will get the volume of a cylinder. </p>

74 <p>Apply the height and radius values and calculate, we will get the volume of a cylinder. </p>

76 <h2>Tips and Tricks for Calculating the Volume of Cylinder</h2>

75 <h2>Tips and Tricks for Calculating the Volume of Cylinder</h2>

77 <p>Understanding and learning the volume of a cylinder feels difficult for kids, but by using the tips and tricks below, kids can easily understand it. </p>

76 <p>Understanding and learning the volume of a cylinder feels difficult for kids, but by using the tips and tricks below, kids can easily understand it. </p>

78 <ul><li>Always remember the formula for the volume of a cylinder. Memorizing it makes the calculations easier.</li>

77 <ul><li>Always remember the formula for the volume of a cylinder. Memorizing it makes the calculations easier.</li>

79 </ul><ul><li>Use 3.14 for the value of ℼ, for simple calculations.</li>

78 </ul><ul><li>Use 3.14 for the value of ℼ, for simple calculations.</li>

80 </ul><ul><li>Don’t do all the calculations in your head, write them step by step to avoid mistakes.</li>

79 </ul><ul><li>Don’t do all the calculations in your head, write them step by step to avoid mistakes.</li>

81 </ul><h2>Common Mistakes and How to Avoid Them in Volume of Cylinder Calculations</h2>

80 </ul><h2>Common Mistakes and How to Avoid Them in Volume of Cylinder Calculations</h2>

82 <p>Making mistakes in calculations is common for kids, by using the following mistakes and the ways to avoid them can help them to avoid those mistakes </p>

81 <p>Making mistakes in calculations is common for kids, by using the following mistakes and the ways to avoid them can help them to avoid those mistakes </p>

83 <h3>Problem 1</h3>

82 <h3>Problem 1</h3>

84 <p>Find the volume of cylinder with radius 8 cm and height 18 cm.</p>

83 <p>Find the volume of cylinder with radius 8 cm and height 18 cm.</p>

85 <p>Okay, lets begin</p>

84 <p>Okay, lets begin</p>

86 <p>3619.2 cm3. </p>

85 <p>3619.2 cm3. </p>

87 <h3>Explanation</h3>

86 <h3>Explanation</h3>

88 <p> Given, radius (r) = 8</p>

87 <p> Given, radius (r) = 8</p>

89 <p>Height (h) = 18</p>

88 <p>Height (h) = 18</p>

90 <p>Using the formula, V = ℼr2h</p>

89 <p>Using the formula, V = ℼr2h</p>

91 <p>V = 3.14159 × 82 × 18 </p>

90 <p>V = 3.14159 × 82 × 18 </p>

92 <p>= 3.14159 × 64 × 18</p>

91 <p>= 3.14159 × 64 × 18</p>

93 <p>= 3619.2 cm3. </p>

92 <p>= 3619.2 cm3. </p>

94 <p>Well explained 👍</p>

93 <p>Well explained 👍</p>

95 <h3>Problem 2</h3>

94 <h3>Problem 2</h3>

96 <p>A cylinder has a diameter of 10 cm and a height of 12 cm. What is the volume?</p>

95 <p>A cylinder has a diameter of 10 cm and a height of 12 cm. What is the volume?</p>

97 <p>Okay, lets begin</p>

96 <p>Okay, lets begin</p>

98 <p>942 cm3.</p>

97 <p>942 cm3.</p>

99 <h3>Explanation</h3>

98 <h3>Explanation</h3>

100 <p>Here, diameter = 10 cm.</p>

99 <p>Here, diameter = 10 cm.</p>

101 <p>Height = 12 cm.</p>

100 <p>Height = 12 cm.</p>

102 <p>Using the formula, V = ℼ(d/2)2h</p>

101 <p>Using the formula, V = ℼ(d/2)2h</p>

103 <p>V = 3.14159 × (10/2)2 × 12 </p>

102 <p>V = 3.14159 × (10/2)2 × 12 </p>

104 <p>= 3.14159 × 52 × 12 </p>

103 <p>= 3.14159 × 52 × 12 </p>

105 <p>= 3.14159 × 25 × 12</p>

104 <p>= 3.14159 × 25 × 12</p>

106 <p>= 942 cm3. </p>

105 <p>= 942 cm3. </p>

107 <p>Well explained 👍</p>

106 <p>Well explained 👍</p>

108 <h3>Problem 3</h3>

107 <h3>Problem 3</h3>

109 <p>The volume of a cylinder is 314 cm3, and the radius is 5 cm. Find the height.</p>

108 <p>The volume of a cylinder is 314 cm3, and the radius is 5 cm. Find the height.</p>

110 <p>Okay, lets begin</p>

109 <p>Okay, lets begin</p>

111 <p>4 cm.</p>

110 <p>4 cm.</p>

112 <h3>Explanation</h3>

111 <h3>Explanation</h3>

113 <p>The formula for cylinder is V = ℼr2h.</p>

112 <p>The formula for cylinder is V = ℼr2h.</p>

114 <p>Here, V = 314</p>

113 <p>Here, V = 314</p>

115 <p>r = 5</p>

114 <p>r = 5</p>

116 <p>V = ℼr2h</p>

115 <p>V = ℼr2h</p>

117 <p>Vℼr2 = h</p>

116 <p>Vℼr2 = h</p>

118 <p>= 314/3.14 × 5 × 5 </p>

117 <p>= 314/3.14 × 5 × 5 </p>

119 <p>= 314/78.5</p>

118 <p>= 314/78.5</p>

120 <p>= 4 cm. </p>

119 <p>= 4 cm. </p>

121 <p>Well explained 👍</p>

120 <p>Well explained 👍</p>

122 <h3>Problem 4</h3>

121 <h3>Problem 4</h3>

123 <p>A water tank is cylindrical that has radius of 2 m and a height of 3 m. How much water can it hold?</p>

122 <p>A water tank is cylindrical that has radius of 2 m and a height of 3 m. How much water can it hold?</p>

124 <p>Okay, lets begin</p>

123 <p>Okay, lets begin</p>

125 <p>37680 liters of water. </p>

124 <p>37680 liters of water. </p>

126 <h3>Explanation</h3>

125 <h3>Explanation</h3>

127 <p> First we will use the volume formula and find the volume of water tank, and then we will convert it to liters so, we can find the total liters of water it holds.</p>

126 <p> First we will use the volume formula and find the volume of water tank, and then we will convert it to liters so, we can find the total liters of water it holds.</p>

128 <p>The formula for volume is V = ℼr2h</p>

127 <p>The formula for volume is V = ℼr2h</p>

129 <p>Here, radius = 2</p>

128 <p>Here, radius = 2</p>

130 <p>height = 3</p>

129 <p>height = 3</p>

131 <p>V = ℼr2h</p>

130 <p>V = ℼr2h</p>

132 <p>= 3.14 × 22 × 3</p>

131 <p>= 3.14 × 22 × 3</p>

133 <p>= 3.14 × 4 × 3</p>

132 <p>= 3.14 × 4 × 3</p>

134 <p>= 37.68 m3.</p>

133 <p>= 37.68 m3.</p>

135 <p>Now converting the m3 to liters, that is 1 cubic meter = 1000 liters.</p>

134 <p>Now converting the m3 to liters, that is 1 cubic meter = 1000 liters.</p>

136 <p>Volume in liters = 37.68 × 1000 = 37680 liters. </p>

135 <p>Volume in liters = 37.68 × 1000 = 37680 liters. </p>

137 <p>Well explained 👍</p>

136 <p>Well explained 👍</p>

138 <h2>What is the volume of cylindrical tanks?</h2>

137 <h2>What is the volume of cylindrical tanks?</h2>

139 <h3>1.What is the volume of cylindrical tanks?</h3>

138 <h3>1.What is the volume of cylindrical tanks?</h3>

140 <p>The volume of the cylindrical tank is V = ℼr2h.</p>

139 <p>The volume of the cylindrical tank is V = ℼr2h.</p>

141 <h3>2.How many volumes in a liter?</h3>

140 <h3>2.How many volumes in a liter?</h3>

142 <p>One litre is equal to the volume of a cubic decimeter. </p>

141 <p>One litre is equal to the volume of a cubic decimeter. </p>

143 <h3>3.What is the total surface area of a cylinder?</h3>

142 <h3>3.What is the total surface area of a cylinder?</h3>

144 <p>The total surface area of a cylinder is TSA = 2ℼr2 + 2ℼrh.</p>

143 <p>The total surface area of a cylinder is TSA = 2ℼr2 + 2ℼrh.</p>

145 <h3>4.What is the volume of a cuboid?</h3>

144 <h3>4.What is the volume of a cuboid?</h3>

146 <p>The volume of a cuboid is: Volume = length × width × height.</p>

145 <p>The volume of a cuboid is: Volume = length × width × height.</p>

147 <h3>5.What is the volume of a sphere?</h3>

146 <h3>5.What is the volume of a sphere?</h3>

148 <p>The volume of the sphere is: Volume = (4/3)ℼr3.</p>

147 <p>The volume of the sphere is: Volume = (4/3)ℼr3.</p>

149 <h2>Important Glossaries of Volume of Cylinder</h2>

148 <h2>Important Glossaries of Volume of Cylinder</h2>

150 <ul><li><strong> Volume -</strong>It is the amount of space inside a 3D shape. It tells how much something can contain or hold.</li>

149 <ul><li><strong> Volume -</strong>It is the amount of space inside a 3D shape. It tells how much something can contain or hold.</li>

151 </ul><ul><li><strong>Radius -</strong>It is the distance from the center of a circle to its edge.</li>

150 </ul><ul><li><strong>Radius -</strong>It is the distance from the center of a circle to its edge.</li>

152 </ul><ul><li><strong>Cylinder -</strong>It is a 3D shape with two flat, circular bases and a curved size. It looks like a can or a tube.</li>

151 </ul><ul><li><strong>Cylinder -</strong>It is a 3D shape with two flat, circular bases and a curved size. It looks like a can or a tube.</li>

153 </ul><ul><li><strong>Pi -</strong>It is the special number used in math to calculate circles. It is approximately 3.14.</li>

152 </ul><ul><li><strong>Pi -</strong>It is the special number used in math to calculate circles. It is approximately 3.14.</li>

154 </ul><p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>

153 </ul><p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>

155 <p>▶</p>

154 <p>▶</p>

156 <h2>Seyed Ali Fathima S</h2>

155 <h2>Seyed Ali Fathima S</h2>

157 <h3>About the Author</h3>

156 <h3>About the Author</h3>

158 <p>Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.</p>

157 <p>Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.</p>

159 <h3>Fun Fact</h3>

158 <h3>Fun Fact</h3>

160 <p>: She has songs for each table which helps her to remember the tables</p>

159 <p>: She has songs for each table which helps her to remember the tables</p>