Question

What is the volume of the largest sphere that you could carve out of a wooden block whose edges measure 8m by 8m by 8m? Use the Pi and round to the nearest tenth.

Answer 1

What is the volume of the largest sphere that you could carve out of a wooden block whose edges measure 8m by 8m by 8m? Use the Pi and round to the nearest tenth.​

In a cube of length side 8 m, the larger diameter of a sphere is 8 m

so

the radius is

r=8/2=4 m

the volume of the sphere is

`V=(4)/(3)\cdot\pi\cdot r^3`

substitute the given values

`\begin{gathered} V=(4)/(3)\cdot\pi\cdot4^3 \\ V=85.33\pi \end{gathered}`

use pi=3.14

V=85.33(3.14)=267.9 m3

volume is 267.9 cubic meters