Question

A toy has various shaped objects that a child can push through matching holes. The area of the square hole is square centimeters. The volume of a​ cube-shaped block is cubic centimeters. a. Which edge length can be​ found? Explain. b. Will the block fit in the square​ hole? Explain.

Answer 1

a. We can find edge length of the cube-shaped bock. b. No, it will not

Explanation:

Here is the complete question

A toy has various shaped objects that a child can push through matching holes. The area of the square hole is 18 square centimeters. The volume of a​ cube-shaped block is 729 cubic centimeters. a. Which edge length can be​ found? Explain. b. Will the block fit in the square​ hole? Explain.

Solution

a.

Since the volume of the cube 729 cm³ is a perfect cube of 9 cm and the area of the square hole which is 18 cm² is not a perfect square, the edge length of the cube-shaped block is easily found.

b. Since the edge length of the block is 9 cm, the area of one of its faces is (9 cm)² = 81 cm² which is greater than the area of the square hole which is 18 cm². Since their dimensions are not the same, the cube-shaped block will not fit into the square hole.