Volume of a Cylinder Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
Two cylinders have the same volume. Cylinder A has radius 3 and height 16. Cylinder B has height 4. Find the radius of Cylinder B.

Solution

  1. 1
    Step 1: Find the volume of Cylinder A: VA=ฯ€(3)2(16)=144ฯ€V_A = \pi (3)^2 (16) = 144\pi.
  2. 2
    Step 2: Set VB=VAV_B = V_A: ฯ€rB2(4)=144ฯ€\pi r_B^2 (4) = 144\pi.
  3. 3
    Step 3: Divide both sides by 4ฯ€4\pi: rB2=36r_B^2 = 36.
  4. 4
    Step 4: rB=6r_B = 6.

Answer

Cylinder B has radius 66.
When two cylinders have the same volume, you can set their volume formulas equal and solve for the unknown dimension. Here, halving the height (from 16 to 4, a factor of 4) requires multiplying the area of the base by 4, which means doubling the radius (since r2r^2 scales by 4 when rr doubles).

About Volume of a Cylinder

The amount of three-dimensional space inside a cylinder, found by multiplying the area of the circular base by the height.

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More Volume of a Cylinder Examples

Example 1 easy

A cylinder has a radius of 4 cm and a height of 10 cm. Find its volume. Use [formula].

Example 2 medium

A cylindrical water tank holds [formula] liters. Its height is 20 m. Find the radius of the tank.

Example 3 easy

A soup can has a diameter of 8 cm and a height of 12 cm. Find the volume. Leave your answer in terms

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