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Volume of Hollow Cylinder: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Volume of Hollow CylinderVolume of Hollow Cylinder: Definition and ExamplesTable of ContentsVolume of a Hollow Cylinder Definition of Volume of a Hollow Cylinder

The volume of a hollow cylinder is the amount of space occupied by the hollow cylinder in three-dimensional space. A hollow cylinder (also known as a cylindrical shell) has an empty space inside with different outer and inner radii. The volume is calculated by finding the difference between the volume of the outer cylinder and the inner cylinder.

A hollow cylinder consists of a rolled surface with circular top and base, and it has some thickness at its peripheral. The two circular bases of a hollow cylinder form annulus rings that are congruent and parallel to each other. The height of the hollow cylinder is the perpendicular distance between these two circular bases.

Formula for Volume of a Hollow Cylinder

The formula to calculate the volume of a hollow cylinder is:

V=π(R2−r2)hV = \pi(R^2 - r^2)hV=π(R2−r2)h

Where:

RRR is the outer radius of the cylinder rrr is the inner radius of the cylinder hhh is the height of the cylinder

This formula can be derived by subtracting the volume of the inner cylinder from the volume of the outer cylinder:

V=πR2h−πr2h=π(R2−r2)hV = \pi R^2h - \pi r^2h = \pi(R^2 - r^2)hV=πR2h−πr2h=π(R2−r2)h

Examples of Volume of a Hollow Cylinder Example 1: Finding the Volume of a Hollow Cylinder with Given Dimensions Problem:

Find the volume of a hollow cylinder with outer radius = 6 units, inner radius = 4 units, and height = 14 units.

Step-by-step solution:

Step 1, Write down the given values for the hollow cylinder.

Outer radius (RRR) = 6 units Inner radius (rrr) = 4 units Height (hhh) = 14 units

Step 2, Use the formula for the volume of a hollow cylinder. Volume (VVV) = π(R2−r2)h\pi(R^2 - r^2)hπ(R2−r2)h cubic units

Step 3, Substitute the given values into the formula. V=227[(6)2−(4)2]×14V = \frac{22}{7}[(6)^2 - (4)^2] \times 14V=722​[(6)2−(4)2]×14

Step 4, Calculate the squares of the radii. V=227(36−16)×14V = \frac{22}{7}(36 - 16) \times 14V=722​(36−16)×14

Step 5, Find the difference between the squared radii. V=227×20×14V = \frac{22}{7} \times 20 \times 14V=722​×20×14

Step 6, Multiply all the numbers to get the final answer. V=22×20×2=880V = 22 \times 20 \times 2 = 880V=22×20×2=880 cubic units

The volume of the given hollow cylinder is 880 cubic units.

Example 2: Calculating the Volume of a Hollow Cylinder with Different Dimensions Problem:

Find the volume of a hollow cylinder where the internal radius is 2 units, the external radius is 3 units, and the height is 10 units

Step-by-step solution:

Step 1, Identify the given values.

Outer radius (RRR) = 3 units Inner radius (rrr) = 2 units Height (hhh) = 10 units

Step 2, Apply the formula for volume of hollow cylinder. V=π(R2−r2)hV = \pi(R^2 - r^2)hV=π(R2−r2)h

Step 3, Substitute the values and calculate the squares. V=π×(9−4)×10V = \pi \times (9 - 4) \times 10V=π×(9−4)×10

Step 4, Calculate the difference between squared radii. V=π×5×10V = \pi \times 5 \times 10V=π×5×10

Step 5, Multiply to get the final answer (using π=3.14\pi = 3.14π=3.14). V=3.14×5×10=157V = 3.14 \times 5 \times 10 = 157V=3.14×5×10=157 cubic units

The volume of the hollow cylinder is 157 cubic units.

Example 3: Finding the Inner Radius of a Hollow Cylinder Problem:

Determine the inner radius of a hollow cylinder whose outer radius is 6 units, height is 10 units and volume is 847.8 cubic units. (Use π=3.14\pi = 3.14π=3.14)

Step-by-step solution:

Step 1, List what we know and what we need to find.

Outer radius (RRR) = 6 units Height (hhh) = 10 units Volume (VVV) = 847.8 cubic units We need to find the inner radius (rrr).

Step 2, Use the volume formula and substitute the known values.

V=π(R2−r2)hV = \pi(R^2 - r^2)hV=π(R2−r2)h 847.8=3.14×(62−r2)×10847.8 = 3.14 \times (6^2 - r^2) \times 10847.8=3.14×(62−r2)×10

Step 3, Simplify the equation.

847.8=3.14×(36−r2)×10847.8 = 3.14 \times (36 - r^2) \times 10847.8=3.14×(36−r2)×10 847.8=31.4×(36−r2)847.8 = 31.4 \times (36 - r^2)847.8=31.4×(36−r2)

Step 4, Solve for (36−r2)(36 - r^2)(36−r2).

847.831.4=36−r2\frac{847.8}{31.4} = 36 - r^231.4847.8​=36−r2 27=36−r227 = 36 - r^227=36−r2

Step 5, Find r2r^2r2 by rearranging the equation.

r2=36−27r^2 = 36 - 27r2=36−27 r2=9r^2 = 9r2=9

Step 6, Take the square root to find rrr.

r=9r = \sqrt{9}r=9​ r=3r = 3r=3 units

The inner radius of the hollow cylinder is 3 units.

Comments(1)FFrenchTutorHopeNovember 4, 2025I've used this definition to teach my students. The formula and examples made it easy for them to grasp the volume of a hollow cylinder concept.

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