Volume Math Example 5

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Example 5

medium
A cylinder has volume 200π200\pi cm³ and height 88 cm. Find its radius.

Solution

  1. 1
    Use the cylinder volume formula: V=πr2hV = \pi r^2 h.
  2. 2
    Substitute: 200π=πr2(8)200\pi = \pi r^2(8), so 200=8r2200 = 8r^2.
  3. 3
    Solve: r2=25r^2 = 25, so r=5r = 5 cm.

Answer

r=5 cmr = 5 \text{ cm}
Reverse volume problems are solved by isolating the missing variable in the volume formula. Dividing by the height and by π\pi leaves the radius squared.

About Volume

The amount of three-dimensional space that an object occupies, measured in cubic units such as cm³.

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More Volume Examples

Example 1 easy

Find the volume of a rectangular prism with length [formula] cm, width [formula] cm, and height [for

Example 2 medium

Find the volume of a cylinder with radius [formula] cm and height [formula] cm. Leave your answer in

Example 3 medium

A cylindrical water tank has radius [formula] m and height [formula] m. Find its volume in cubic met

Example 4 hard

A rectangular storage box is [formula] cm long and [formula] cm wide. If its volume is [formula] cm³

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