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 dropdown is a perfect dropdown the length of each edge of the dropdown can be found. each edge is blank centimeters long. square, cube,

Explanation:

Part a

Step1: Recall cube volume formula

The volume \( V \) of a cube is given by \( V = s^3 \), where \( s \) is the edge length.

Step2: Solve for edge length

We know \( V = 27 \, \text{cm}^3 \). So, we solve \( s^3 = 27 \). Taking the cube root of both sides, \( s=\sqrt[3]{27} \). Since \( 3\times3\times3 = 27 \), \( s = 3 \) cm.
The first blank: "volume" (because we use the volume of the cube to find the edge length), the second blank: "cube" (referring to the cube - shaped block), the third blank: "3".

Part b

First, find the side length of the square hole. The area of a square is \( A = l^2 \), where \( l \) is the side length. Given \( A = 6 \, \text{cm}^2 \), \( l=\sqrt{6}\approx2.45 \) cm. The edge length of the cube is 3 cm. Since \( 3>2.45 \), the cube - shaped block will not fit through the square hole.

Answer:

3