Question

A pyramid with a square base with dimensions 12 by 7 is shown. A cone is cut out of the center of the pyramid. The cone has a height of 10 and a diameter of 6.
Which expressions represent the volume of the composite figure (the shaded figure)? Check all that apply.

(7)(12)(10) – π(32)(10)
One-third(7)(12)(10) – One-thirdπ(32)(10)
One-third(7)(12)(10) + One-thirdπ(32)(10)
280 – 30π
280 + 30π
840 – 90π

Answer 1

Correct expressions:
- One-third(7)(12)(10) – One-thirdπ(3^2)(10)
- 280 – 30π

Work:
- Pyramid: V = (1/3)(base area)(height) = (1/3)(7·12)(10) = 280.
- Cone: V = (1/3)πr^2h with r = 3, h = 10 → (1/3)π(3^2)(10) = 30π.
- Composite (pyramid minus cone) = 280 − 30π.

(The options (7)(12)(10) – π(3^2)(10) and 840 – 90π are 3 times too large; the “+” versions give the wrong sign.)