Find the volume of the oblique prism in cubic inches.
Pythagoras and Cavalieri are important names to remember. And not just because they're fun to say.
V ≈ 418.3 in3
How many liters of water will fit into this swimming pool? Assume that 1 cubic foot equals about 28.3 liters.
Think of the pool as two rectangular prisms. Add the volumes of both prisms and then convert feet to liters.
The pool can fit 23,232 liters of water. Or liters of anything we want, really.
A regular right pentagonal prism has a perimeter of 10 cm3 and a height of 8 cm3. What is its density of the prism if it weighs 110 grams?
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. Density is just mass over volume.
The density of the prism is about 2 grams per cubic centimeter.
Make it rain.