### Home > GC > Chapter 11 > Lesson 11.2.2 > Problem11-87

11-87.

Find the volume of the large pyramid.

$V = \frac{1}{3} (\text{volume of corresponding prism})$

$V = \frac{1}{3}(9 \cdot 9 \cdot 12) = 324\text{ cm}^3$

$\text{The side of the small pyramid is } \frac{1}{3} \text{ the side of the large pyramid, because }3 \text{ is } \frac{1}{3} \text{ of } 9.$

$\text{So, the lsf is } \frac{1}{3}.$

Find the volume of the small pyramid.

(volume larger)(lsf)3 = volume smaller

$324 \cdot \left(\frac{1}{3}\right)^3 = 324 \cdot \frac{1}{27} = 12\text{ cm}^3$

Subtract the volume of the smaller pyramid from the volume of the larger pyramid.

324 − 12

312 cm3