Find the volume of a sphere if its circumference is 37.7 inches.
Hint
Use the circumference to find the radius. Use the radius to find the volume. Then you're home free.
Answer
V ≈ 904.8 in3
Example 2
Find the volume of the sphere.
Hint
Remember the formula and you're golden.
Answer
V ≈ 50,965 mm3
Example 3
Find the volume of the following solid, a cylinder with a hemispherical chunk removed. The radius is 18 meters.
Hint
Find the volume of the cylinder and then subtract the volume of the hemisphere.
Answer
V ≈ 24,429 m3
Example 4
Find the volume of the capsule. If it contains 500 milligrams of aspirin, what is the density of the aspirin?
Hint
Density is mass over volume. To find density, we need volume.
Answer
The volume of the capsule is about 172 mm3 and the density of aspirin is approximately 2.9 mg/mm3.
Example 5
Super Sourz candy will make you cry faster than a broken nose. The box has dimensions of 4 inches, 6 inches, and 10 inches. If it's filled with small spherical Super Sourz candies, each with a diameter of 1.4 inches, how many candies does the box contain?
Hint
Find the volume of the box and the volume of one candy. Then see how many candy volumes fit into the box volume.
Answer
The volume of the box is 240 cubic inches and one Super Sourz candy is about 1.4 cubic inches (don't forget to slice that diameter in half before finding the spherical volume). One box has about 167 Super Sourz candies. Cue tears of joy and sourness.
Example 6
If the surface area of Planet Earth is about 196,712,612 square miles, what is its volume? Go ahead and pretend with us that the Earth is a perfect sphere.
Hint
The radius is all we need, and we can find it using the surface area: SA = 4πr2.
Answer
The earth's volume is about 259,431,149,227 cubic miles. Most of it is liquid hot magma.
Example 7
When picking a bowling ball, you don't want it to be too heavy or too light. A black shiny bowling ball has a circumference of 25.1 inches. If the density of the bowling ball is 0.0448 lbs/in3, how much does it weigh?
Hint
To get the weight, just put the ball on a scale. If it keeps rolling off, you can try multiplying the volume and the density together.
Answer
The bowling ball weighs about 12 pounds. Now put on those clowny bowling shoes and kick some bowling butt.
