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

$b^{2} = 8 \\b= \sqrt{8} \ cm\\b= 2\sqrt{2} \ cm$

the answer Part a) is

the length side of the square is $2\sqrt{2} \ cm$

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 $4\ cm$