Question

1. kai is making a chessboard using pieces of wood that measure 1 square inch. when he finishes, the chessboard will have an area of 64 square inches. how many pieces of wood should he put along each side?

a 64 pieces of wood
b 64² pieces of wood
c 8 pieces of wood
d 8² pieces of wood

Explanation:

Problem 1:

Step1: Recall the volume formula for a cube.

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

Step2: Substitute the given volume and solve for \( s \).

We know \( V = 125 \) cubic inches. So, we set up the equation \( s^3 = 125 \). To find \( s \), we take the cube root of both sides. The cube root of 125 is 5 because \( 5^3 = 125 \). So, \( s=\sqrt[3]{125} = 5 \) inches.

Step1: Recall the area formula for a square.

The area \( A \) of a square with side length \( s \) is given by \( A = s^2 \).

Step2: Substitute the given area and solve for \( s \).

We know the area of the chessboard (a square) is 64 square inches. So, we set up the equation \( s^2 = 64 \). To find \( s \), we take the square root of both sides. The square root of 64 is 8 because \( 8^2 = 64 \). This \( s \) represents the number of 1 - square - inch pieces along each side.

Answer:

The length of each edge is 5 inches.

Problem 2: