What's the volume of a cylinder with a base diameter of 10 mm and a height of 3.5 mm?
Hint
A cylinder's volume is always V = πr2h. The problem gives us the diameter, though.
Answer
V ≈ 274.9 mm3
Example 2
If the total volume of this figure is 788,500 cubic feet, then how tall is the cylindrical tower?
Hint
Subtract the volume of the rectangular prism and then use the volume formula of a cylinder to figure out the rest.
Answer
The tower is about 150 feet tall.
Example 3
You built a Pacman-shaped piggybank out of a 1 ft × 1 ft block of wood in your woodshop class. In cubic feet, how much room does your Pacman piggybank have for coins?
Hint
Out of the total 360° rotation at the center of the cylinder, 120° is one-third of that value. That means we've removed one third of the volume of the whole cylinder.
Answer
The Pacman bank contains about 0.52 ft3 of space for coins. Maybe consider making a Ms. Pacman one as well.
Example 4
You have 700 jellybeans. (Yes, you counted them all because it was more fun than doing your geometry homework.) You're given a cylindrical cup with a radius of 3 inches and a height of 10 inches. If each jellybean is about 0.5 cubic inches in volume, will you be able to fit all the jellybeans into the cup? If not, how many will be left over?
Hint
We can convert cubic inches to jellybeans using the ratio that 1 jellybean = 0.5 cubic inches. Wouldn't it be great if everything in life could be measured in jellybeans?
Answer
You'd only be able to fit about 565 jellybeans into the cup, meaning 135 jellybeans will be left over. Guess you'll just have to eat them.
Example 5
This rectangular prism has an oblique cylinder cut out of it. Find the volume of the solid if the diameter of the cylinder is 20 m, the base of the prism is a square with side length 40 m, and the length of the prism is 115 m.
Hint
Cavalieri says, "Only the height of the cylinder is important!" Or he would, anyway, if he weren't born 400 years ago.
