Unit 5, Lesson 20
The Volume of a Sphere
Grade 8
Practice
Problem 1
-
A cube’s volume is 512 cubic units. What is the length of its edge?
-
If a sphere fits snugly inside this cube, what is its volume?
-
What fraction of the cube is taken up by the sphere? What percentage is this? Explain or show your reasoning.
to access Practice Problem Solutions.
Problem 2
Sphere \(A\) has radius 2 cm. Sphere \(B\) has radius 4 cm.
- Calculate the volume of each sphere.
- The radius of Sphere \(B\) is double that of Sphere \(A\). How many times greater is the volume of Sphere \(B\)?
to access Practice Problem Solutions.
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.
to access Practice Problem Solutions.
Problem 4
Match the description of each sphere to its correct volume.
Sphere A: radius of 4 cm
Sphere B: diameter of 6 cm
Sphere C: radius of 8 cm
Sphere D: radius of 6 cm
\(288\pi\) cm3
\(\frac{256}3 \pi\) cm3
\(36\pi\) cm3
\(\frac {2,048}3 \pi\) cm3
to access Practice Problem Solutions.
Problem 5
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.
to access Practice Problem Solutions.