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Volume Relationships of 3D Shapes

Volume Relationships of 3D Shapes

Assessment

Interactive Video

•

Mathematics, Physics, Science

•

9th - 10th Grade

•

Practice Problem

•

Hard

Created by

Thomas White

FREE Resource

The video tutorial covers the estimation of a hemisphere's volume by comparing it with a cylinder and a cone. It begins with calculating the volume of a cylinder with a radius and height of 5 units, resulting in 125π. The tutorial then discusses estimating the hemisphere's volume, which is smaller than the cylinder's but larger than the cone's. The cone's volume is calculated as 125/3π. The lesson concludes by comparing the volumes and emphasizing that the hemisphere's volume lies between the cone's and the cylinder's volumes.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the relationship between the radius of the hemisphere and the cylinder?

The radius of the hemisphere is twice that of the cylinder.

The radius of the hemisphere is half that of the cylinder.

The radius of the hemisphere is unrelated to the cylinder.

The radius of the hemisphere is the same as that of the cylinder.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you calculate the volume of a cylinder?

V = 2πrh

V = πr²h

V = 1/3πr²h

V = 4/3πr³

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the volume of a cylinder with a radius and height of 5 units?

75π

150π

100π

125π

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How does the volume of the hemisphere compare to the cylinder?

The hemisphere is equal to the cylinder.

The hemisphere is smaller than the cylinder.

The hemisphere is unrelated to the cylinder.

The hemisphere is larger than the cylinder.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the formula for the volume of a cone?

V = 4/3πr³

V = πr²h

V = 1/3πr²h

V = 2/3πr²h

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the volume of a cone with a radius of 5 units and height of 5 units?

70π

60π

50π

41 2/3π

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which shape has the smallest volume: the cone, the hemisphere, or the cylinder?

The cone

The hemisphere

They all have the same volume

The cylinder

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