Find the volumes of the cylinder and the cone separately. Then add them together. Then do the next problem.
Answer
V ≈ 1,130,974 ft3
Example 3
The solid is a section of a cone. Find its volume.
Hint
Imagine slicing the top off a big cone. What would the sliced-off part look like? Also, what if we told you the ratio of the height difference to the radius difference stays constant?
Answer
V ≈ 364,803 mm3
Example 4
Your little sister wants to dress up as a fairy for Halloween and she needs you to go shopping with her. At the store, she finds this fairy hat in the shape of a cone and wants you to pay for it. You can't help imagining filling the hat with ice-cold water and dumping it on her. If the circumference of the hat's base is 18 inches, how much water would you dump on her?
Hint
Since the angle of the lateral area with the base is 60°, either trigonometry or knowledge of special triangles will help find the volume of (imaginary) ice-cold water that you'd be (imagining) dumping on her.
Answer
You'd imagine splashing her with 42.3 in3 of cold water. Instead, you'll just pay the $9.95 for the stinkin' hat.
Example 5
The world's largest double-sided pencil is perfectly cylindrical with the tips taking the shapes of identical cones on both ends. If wood weighs 50 pounds per cubic foot, how heavy is the pencil? Assume the pencil is made entirely of wood.
Hint
Find the volume of the entire pencil, and then convert cubic fee to pounds.
Answer
The entire pencil is about 2261.9 cubic feet and weighs approximately 113,095 pounds. That's a lot of wood.
