18. 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 valume of a cube-shaped block is 64 cubic centimeters. Part A Which edge length can you find? Explain. PART 8 Will the block fit in the square hole? Explain.

Given: - The area of the square hole is 8 square centimeters. - The volume of the cube-shaped block is 64 cubic centimeters. Part A: To find the edge length of the cube-shaped block, we can use the formula for the volume of a cube: \[ V = a^3 \] where \( V \) is the volume and \( a \) is the edge length. Given that the volume of the cube-shaped block is 64 cubic centimeters, we can set up the equation: \[ 64 = a^3 \] To find the edge length \( a \), we need to solve for \( a \) in the equation \( 64 = a^3 \). Solve the equation by following steps: - step0: Solve for \(a\): \(64=a^{3}\) - step1: Swap the sides: \(a^{3}=64\) - step2: Simplify the equation: \(\sqrt[3]{a^{3}}=\sqrt[3]{64}\) - step3: Calculate: \(a=\sqrt[3]{64}\) - step4: Evaluate: \(a=4\) The edge length of the cube-shaped block is 4 centimeters. Part B: To determine if the block will fit in the square hole, we need to compare the area of the square hole with the area of the base of the cube-shaped block. The area of the square hole is 8 square centimeters. The area of the base of the cube-shaped block is \( a^2 \), where \( a \) is the edge length of the cube. Since the edge length of the cube is 4 centimeters, the area of the base of the cube-shaped block is \( 4^2 = 16 \) square centimeters. Since the area of the square hole (8 square centimeters) is less than the area of the base of the cube-shaped block (16 square centimeters), the block will not fit in the square hole.