Answer to Question #349431 in Geometry for hatdog

Question

In a rectangular parallelepiped, the length and the width of the base are 12 in. and 9

in., respectively. Find the volume if the length of the diagonal of the solid is 25 inches.

Answer 1

Given $a=12\ in, b=9 \ in, \sqrt{a^2+b^2+c^2}=25\ in.$

Substitute

$$12^2+9^2+c^2=25^2$$

$$c^2=400, c>0$$

$$c=20\ in$$

$$V=abc=12(9)(20)=2160({in}^3)$$

2160 cubic inches