Question

A right pyramid has a square base with area 288 square cm. Its peak is 15 cm from each of the other vertices. What is the volume of the pyramid, in cubic centimeters

Answer 1

The volume of the right pyramid is 864 cm³.

The given parameters;

• Base area of the right pyramid, b = 288 cm²
• Slant height of the pyramid, L = 15 cm

What is volume of right pyramid?

The volume of a right pyramid is one-third the product of the base and the perpendicular height.

The diagonal length of the right pyramid is calculated as follows;

$d^2 = b^2 + b^2\\\\ d^2 = (\sqrt{288})^2 + (\sqrt{288} )^2 \\\\ d ^2 = 576\\\\ d = \sqrt{576} \\\\ d = 24 \ cm$

The perpendicular height of the right pyramid is calculated as follows;

$(\frac{d}{2} )^2 + h^2 = 15^2\\\\ (\frac{24}{2})^2 + h^2 = 15^2\\\\ 144 + h^2 = 225\\\\ h^2 = 225-144\\\\ h^2 = 81\\\\ h = \sqrt{81} \\\\ h = 9 \ cm$

The volume of the right pyramid is calculated as follows;

$V = \frac{1}{3} \times b \times h\\\\ V = \frac{1}{3} \times 288 \times 9\\\\ V = 864 \ cm^3$

Learn more about volume of the right pyramid here: brainly.com/question/1273042