Question

1. a toy has various shaped objects that a child can push through matching holes. the area of the square hole is 8 square centimeters. the volume of a cube - shaped block is 64 cubic centimeters. 8.ns0.1.7 part a which edge length can you find? explain. part b will the block fit in the square hole? explain.

Explanation:

Step1: Find the edge - length of the cube

The volume formula for a cube is $V = s^{3}$, where $V$ is the volume and $s$ is the edge - length. Given $V=64$ cubic centimeters. We solve the equation $s^{3}=64$. Taking the cube - root of both sides, $\sqrt[3]{s^{3}}=\sqrt[3]{64}$, so $s = 4$ centimeters.

Step2: Find the side - length of the square hole

The area formula for a square is $A = a^{2}$, where $A$ is the area and $a$ is the side - length. Given $A = 8$ square centimeters. We solve the equation $a^{2}=8$, so $a=\sqrt{8}=2\sqrt{2}\approx2.83$ centimeters.

Step3: Compare the edge - length of the cube and the side - length of the square hole

The edge - length of the cube $s = 4$ centimeters and the side - length of the square hole $a\approx2.83$ centimeters. Since $4>2.83$, the block will not fit through the square hole.

Answer:

PART A: The edge - length of the cube is 4 centimeters. We found this by using the volume formula for a cube $V = s^{3}$ and solving for $s$ when $V = 64$ (i.e., $s=\sqrt[3]{64}=4$).
PART B: The block will not fit in the square hole. The edge - length of the cube is 4 centimeters and the side - length of the square hole is $\sqrt{8}\approx2.83$ centimeters, and $4>2.83$.