Question

A lab technician made a 14 cm diameter hole through the middle of a cylinder that has a diameter of 20 cm and a height of 18 cm. What is the approximate volume of the finished cylinder, to the nearest tenth of a centimeter?

Answer 1

`2,882.5\ cm^3`

Explanation:

we know that

The approximate volume of the finished cylinder, is equal to subtract the volume of the hole from the volume of the original cylinder

so

`V=\pi r_1^(2)h-\pi r_2^(2)h`

`V=\pi h[r_1^(2)-r_2^(2)]`

where

r_1 is the radius of the original cylinder

r_2 is the radius of the hole

we have

`r_1=20/2=10\ cm` ---> the radius is half the diameter

`r_2=14/2=7\ cm` ---> the radius is half the diameter

`h=18\ cm`

`\pi=3.14`

substitute the given values in the formula

`V=(3.14)(18)[10^(2)-7^(2)]`

`V=56.52[51]\\V=2,882.5\ cm^3`