Question

The base edges of a right parallelepiped whose altitude is 8 in., measures 12 in. and

15 in. If the angle included by these edges is 135°, find the volume and the total

surface area of the solid

Answer 1

Volume $=$ L$\times$ W$\times$ H

8$\times$ 12$\times$ H$($ cos$\Theta$ $)$

8$\times$ 12$\times$ $($ 0.7071$\times$ 15$)$

Answer is:

1018.234in$^{3}$

Area;

A$=$ 2$($ ab+ac+bc$)$

2 $($ 8$\times$ 12$)$ $+($ 8$\times$ 15$)+$ $($ 12$\times$ 15$)$

2$($ 96 $+$ 120$+$ 180$)$

Answer is;

796in$^{2}$