Question

The area of the square hole is 8 square centimeters. The volume of a cube shaped block is 64 cubic centimeters. Which edge length can you find?

Answer 1

case a) The area of the square hole is 8 square centimeters

we know that

the area of a square is equal to

`A=b^(2)`

where

b is the length side of the square

in this problem we have

`A=8\ cm^(2)`

Find the length side b

`b^(2) = 8 \\b= √(8) \ cm\\b= 2√(2) \ cm`

the answer Part a) is

the length side of the square is
`2√(2) \ cm`

Part b) The volume of a cube shaped block is 64 cubic centimeters

we know that

the volume of a cube is equal to

`V=b^(3)`

where

b is the length side of the cube

in this problem we have

`V=64\ cm^(3)`

Find the length side b

`b^(3) = 64 \\b= \sqrt[3]{64} \\b= 4\ cm`

therefore

the answer Part b) is

the length side of the cube is
`4\ cm`