Question

a toy has various shaped objects that a child can push through matching holes. the area of the square hole is 6 square centimeters. the volume of a cube - shaped block is 27 cubic centimeters. a. which edge length can be found? explain. b. will the block fit in the square hole? explain. a. since 27 is a perfect cube, the length of each edge of the block can be found. each edge is 3 centimeters long. b. the area of one face of the block is square centimeters. since this is smaller/larger than the area of the hole, the block will/will not fit in the hole.

Explanation:

Step1: Find the area of one - face of the cube

The volume of the cube $V = s^3$, where $s$ is the edge - length. Given $V = 27$ cm³, so $s=\sqrt[3]{27}=3$ cm. The area of one face of the cube $A_{cube}=s^2$. Substituting $s = 3$ cm, we get $A_{cube}=3^2 = 9$ square centimeters.

Step2: Compare the area of the face of the cube and the area of the hole

The area of the square hole is $A_{hole}=6$ square centimeters. Since $9>6$, the area of one face of the block is larger than the area of the hole, so the block will not fit in the hole.

Answer:

b. The area of one face of the block is 9 square centimeters. Since this is larger than the area of the hole, the block will not fit in the hole.