Question

Find the height of the cone when the volume=300(pie) and the radius is 12

Answer 1

The height of this cone is

`\displaystyle (25)/(4)`,

which is the same as 6.25 in decimals.

Explanation:

Consider the formula for the volume
`V` of a cone:

`\displaystyle V = (1)/(3) \pi\cdot r^(2)\cdot h`,

where

• 
  `r` is the radius of the base of the cone, and
• 
  `h` is the height of the cone.

For this cone,

• 
  `V = 300\;\pi`,
• 
  `r = 12`, and
• 
  `h` is to be found.

Rearrange the equation to find the height of this cone.

`\displaystyle V = (1)/(3) \pi\cdot r^(2)\cdot h`,

`3\;V = \pi \cdot r^(2)\cdot h`,

`\displaystyle (3\;V)/(\pi\cdot r^(2)) = h`.

Therefore,

`h = \displaystyle (3\;V)/(\pi\cdot r^(2)) = \frac{3* 300\;\pi}{{12}^(2)\; \pi} = (25)/(4) = 6.25`.