Find the volume of the oblique prism in cubic inches.
Hint
Here's a little trick: even though this prism is all slanted and refuses to stand up straight, its volume formula is still just the area of the base times the height. We'll need to pay a quick visit to our main man Pythagoras to find the height, though.
Answer
V ≈ 418.3 in3
Example 2
How many liters of water will fit into this swimming pool? Assume that 1 cubic foot equals about 28.3 liters.
Hint
Think of the pool as two rectangular prisms. Add the volumes of both prisms and then convert feet to liters.
Answer
The pool can fit 163,008 liters of water. Or liters of anything we want, really.
Example 3
A regular right pentagonal prism has a perimeter of 10 cm and a height of 8 cm. What's the volume of the prism?
Hint
The pentagon is made up of 5 triangles with bases equal to the edges and heights from the center of the pentagon down perpendicular to the edges. Think back to those handy trig ratios to find the height of each triangle.
