Multiple choice

A regular right square pyramid has a square base with side length 16 cm and a slant height of 10 cm. What is the volume of the pyramid?

  1. 384 cm3

  2. 448 cm3

  3. 512 cm3

  4. 576 cm3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The height h of the pyramid is found using the slant height s=10 and half the base side a/2=8. By Pythagorean theorem, h = sqrt(10^2 - 8^2) = sqrt(100 - 64) = sqrt(36) = 6 cm. The volume is (1/3) * base_area * height = (1/3) * (16 * 16) * 6 = 256 * 2 = 512 cm^3.

AI explanation

First, find the vertical height of the pyramid using the Pythagorean theorem on the right triangle formed by the vertical height, half the base side, and the slant height. The slant height is 10 cm and half the base is 8 cm, so the vertical height is the square root of (10 squared minus 8 squared), which equals 6 cm. The volume of a pyramid is calculated as one-third times the base area times the vertical height. Substituting the known values gives one-third times (16 squared) times 6, which simplifies to 256 times 2, resulting in a volume of 512 cm3.

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