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.

Answer 1

The side length of the square hole is about 4.24 cm, while the edge length of the cube-shaped block is 9 cm. Thus, the cube-shaped block will not fit through the square hole.

Step-by-step explanation:

The edge lengths that can be found are the sides of the cube and the square hole. Given that the area of the square hole is 18 square centimeters, we can calculate its side length by taking the square root of the area: √18 cm² which is approximately 4.24 cm. For the cube-shaped block with a volume of 729 cubic centimeters, to find its edge length, we take the cube root of the volume: ∛729 cm³ which is 9 cm.

Will the block fit in the square hole? Considering that the edge length of the block (9 cm) is greater than the side length of the square hole (about 4.24 cm), the block will not fit through the square hole.