A right pyramid has a square base with a perimeter of 24\text{ cm} and a vertical height o… — JAMB UTME

A right pyramid has a square base with a perimeter of $24\text{ cm}$ and a vertical height of $10\text{ cm}$ . What is the volume of the pyramid?

The volume of the pyramid is

120\text{ cm}^3

The volume of a right pyramid is given by

V = \frac{1}{3} \times \text{Base Area} \times h

. First, find the side length of the square base by dividing the perimeter by 4:

s = 24 / 4 = 6\text{ cm}

. The base area is

s^2 = 36\text{ cm}^2

. Substituting into the volume formula gives

V = \frac{1}{3} \times 36 \times 10 = 120\text{ cm}^3

Determine the side length of the square base from its perimeter.

Side length

s = \frac{24\text{ cm}}{4} = 6\text{ cm}

A square has four equal sides, so perimeter divided by 4 yields the side length.

Calculate the area of the square base.

Base Area

A = s^2 = 6^2 = 36\text{ cm}^2

The area of a square is given by the side length squared.

Apply the volume formula for a right pyramid.

Volume

V = \frac{1}{3} \times A \times h = \frac{1}{3} \times 36\text{ cm}^2 \times 10\text{ cm} = 120\text{ cm}^3

The volume of any pyramid is one-third of the base area multiplied by the vertical height.

Volume of a Right Pyramid

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