Lesson 20

The Volume of a Sphere

View Student Lesson

Problem 1

  1. A cube’s volume is 512 cubic units. What is the length of its edge?

  2. If a sphere fits snugly inside this cube, what is its volume?

  3. What fraction of the cube is taken up by the sphere? What percentage is this? Explain or show your reasoning.

Solution

For access, consult one of our IM Certified Partners.

Problem 2

Sphere A has radius 2 cm. Sphere B has radius 4 cm.

  1. Calculate the volume of each sphere.
  2. The radius of Sphere B is double that of Sphere A. How many times greater is the volume of B?

Solution

For access, consult one of our IM Certified Partners.

Problem 3

Three cones have a volume of \(192\pi\) cm3. Cone A has a radius of 2 cm. Cone B has a radius of 3 cm. Cone C has a radius of 4 cm. Find the height of each cone.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 5, Lesson 16.)

Problem 4

The graph represents the average price of regular gasoline in the United States in dollars as a function of the number of months after January 2014.

Coordinate plane, horizontal, months after January 2014, 0 to 36 by fours. Vertical, average price of gas in dollars, 1.6 to 4 by point fours. Graph shows decline, 3 peaks. Please ask for assistance.
  1. How many months after January 2014 was the price of gas the greatest?
  2. Did the average price of gas ever get below $2?
  3. Describe what happened to the average price of gas in 2014.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 5, Lesson 5.)

Problem 5

Match the description of each sphere to its correct volume.

A:

Sphere A: radius of 4 cm

B:

Sphere B: diameter of 6 cm

C:

Sphere C: radius of 8 cm

D:

Sphere D: radius of 6 cm

1:

\(288\pi\) cm3

2:

\(\frac{256}3 \pi\) cm3

3:

\(36\pi\) cm3

4:

\(\frac {2048}3 \pi\) cm3

Solution

For access, consult one of our IM Certified Partners.

Problem 6

While conducting an inventory in their bicycle shop, the owner noticed the number of bicycles is 2 fewer than 10 times the number of tricycles. They also know there are 410 wheels on all the bicycles and tricycles in the store. Write and solve a system of equations to find the number of bicycles in the store.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 4, Lesson 15.)