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6-8 Accelerated 7 Unit 6 Lesson 20

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IM K-5 Math
IM 6-8 Math
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Unit 6, Lesson 20

The Volume of a Sphere

Accelerated 7

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.

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Lesson 20 Resources

Student Materials

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 \(B\)?

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Problem 3

ForLesson 16: Finding Cone Dimensions

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.

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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

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Problem 5

ForLesson 17: Writing Systems of Equations

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.

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