Question

A toy has a various shaped objects that a child can push through matching holes.the area of the square hole is 6square centimeters.The volume of the cube shaped block is 27 cubic centimeters/A.which edge length can be found?/B.Will block fit in the square hole?

Answer 1

Explanation:

The edge length of the square hole = √6 which is 2.45 cm to the nearest hundredth.

The length of each edge of the cube = ∛27 = 3 cm.

So, the block will not fit in the square hole.

Answer 2

A. To find the edge length of the cube-shaped block, we can use the formula for the volume of a cube:

Volume = (Edge Length)^3

Given that the volume of the cube-shaped block is 27 cubic centimeters, we can set up the equation as follows:

27 = (Edge Length)^3

To solve for the edge length, we need to find the cube root of both sides of the equation:

∛27 = ∛(Edge Length)^3

Simplifying:

3 = Edge Length

Therefore, the edge length of the cube-shaped block is 3 centimeters.

B. The area of the square hole is given as 6 square centimeters. To determine if the cube-shaped block will fit in the square hole, we need to compare the dimensions.

The area of a square is calculated by squaring the length of one of its sides. In this case, the area of the square hole is given as 6 square centimeters.

If we assume that the square hole has sides of length x, then we have the equation:

x^2 = 6

To find the value of x, we can take the square root of both sides of the equation:

√(x^2) = √6

Simplifying:

x = √6

Using a calculator, we can approximate the value of √6 to be approximately 2.449.

Since the edge length of the cube-shaped block is 3 centimeters, which is greater than the length of the sides of the square hole (approximately 2.449 centimeters), we can conclude that the cube-shaped block will not fit in the square hole.