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Volume of Spheres and Cylinders




 

Videos and solutions to help Grade 8 students learn the volume formulas for spheres and cylinders.


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Common Core For Grade 8

New York State Common Core Math Module 5, Grade 8, Lesson 11


Lesson 11 Student Outcomes

• Students know the volume formula for a sphere as it relates to a right circular cylinder with the same diameter and height.
• Students apply the formula for the volume of a sphere to real-world and mathematical problems.

Lesson 11 Summary

The formula to find the volume of a sphere is directly related to that of the right circular cylinder. Given a right circular cylinder with radius r and height h, which is equal to 2r, a sphere with the same radius r has a volume that is exactly two-thirds of the cylinder.
Therefore, the volume of a sphere with radius has a volume given by the formula V = 4/3 &pir;r3

Lesson 11 Classwork

Exercises 1–3
1. What is the volume of a cylinder?
2. What is the height of the cylinder?
3. If volume(sphere) = 2/3 volume (cylinder with same radius and height) what is the formula for the volume of a sphere?

Example 1
Compute the exact volume for the sphere shown below.

Example 2
A cylinder has a diameter of 16 inches and a height of 14 inches. What is the volume of the largest sphere that will fit into the cylinder?

Exercises 4–8
4. Use the diagram and the general formula to find the volume of the sphere.

5. The average basketball has a diameter of 9.5 inches. What is the volume of an average basketball? Round your answer to the tenths place.

6. A spherical fish tank has a radius of 8 inches. Assuming the entire tank could be filled with water, what would the volume of the tank be? Round your answer to the tenths place.

7. Use the diagram to answer the questions.
a. Predict which of the figures below has the greater volume. Explain.
b. Use the diagram to find the volume of each and determine which has the larger volume.

8. One of two half spheres formed by a plane through the spheres center is called a hemisphere. What is the formula for the volume of a hemisphere?




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