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.

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.

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.

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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.