Question

A rectangular prism with a square base has a height of 17.2cm and a volume of 24.768cm². What is the length of its base?

Answer 1

Let x be the length of the base of the rectangular prism.

The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.

In this problem, we know that the height is 17.2 cm, and the volume is 24.768 cm³. We also know that the base is a square, so the length and width are the same.

Therefore, we can write the equation:

24.768 = x² * 17.2

To solve for x, we can divide both sides by 17.2, and then take the square root of both sides:

x² = 24.768 / 17.2

x² = 1.44

x = sqrt(1.44)

x = 1.2

Therefore, the length of the base of the rectangular prism is 1.2 cm.

Answer 2

Let's use the formula for the volume of a rectangular prism to solve for the length of the base.

The formula for the volume of a rectangular prism is:

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

We know that the height of the rectangular prism is 17.2 cm, and the volume is 24.768 cm³. We also know that the base is a square, so the length and width are the same. Let's call the length of the base x.

Then, we can write:

V = lwh
24.768 = x * x * 17.2
24.768 = 17.2x²
x² = 1.44
x = 1.2

Therefore, the length of the base of the rectangular prism is 1.2 cm.