Question

volume of pyramids practice

Answer 1

[AI-generated answer — Bot GPT 3.5]

1. Find the volume of a pyramid with a triangular base that has a base length of 6 cm and a height of 4 cm.

Volume = (1/3) * base area * height
Base area = (1/2) * base length * base height
Base area = (1/2) * 6 cm * 4 cm = 12 cm^2

Volume = (1/3) * 12 cm^2 * 4 cm = 16 cm^3

Therefore, the volume of the pyramid is 16 cubic centimeters.

2. Find the volume of a pyramid with a square base that has a base side length of 8 cm and a height of 5 cm.

Volume = (1/3) * base area * height
Base area = base side length^2 = 8 cm * 8 cm = 64 cm^2

Volume = (1/3) * 64 cm^2 * 5 cm = 106.6 cm^3

Therefore, the volume of the pyramid is 106.6 cubic centimeters.

3. A pyramid has a triangular base with sides of lengths 10 cm, 12 cm, and 14 cm, and a height of 8 cm. Calculate the volume of the pyramid.

First, calculate the area of the triangular base using Heron's formula:

s = (10 + 12 + 14) / 2 = 18 cm
Base area = sqrt[18(18-10)(18-12)(18-14)] = sqrt(18*8*6*4) = 24 cm^2

Volume = (1/3) * base area * height
Volume = (1/3) * 24 cm^2 * 8 cm = 64 cm^3

Therefore, the volume of the pyramid is 64 cubic centimeters.