Volume of Cones and Pyramids

Volume of Cones and Pyramids

Assessment

Interactive Video

Mathematics, Physics, Science

9th - 10th Grade

Practice Problem

Hard

Created by

Patricia Brown

FREE Resource

This video tutorial covers the calculation of volumes for pyramids, cones, and spheres. It begins with an introduction to the concept of volume in 3D shapes, focusing on pyramids and their base area and height. The tutorial then explains how cones are a special case of pyramids with a circular base, followed by the formula for the volume of spheres. It also includes calculations for hemispheres and frustums, and concludes with a problem involving the conversion of a sphere's volume into a cone's volume to determine the cone's height.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the volume of a pyramid if the base area is 30 square units and the height is 9 units?

120 cubic units

60 cubic units

270 cubic units

90 cubic units

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If a pyramid has a square base with side length 10 cm and a height of 8 cm, what is its volume?

300 cm³

400 cm³

500 cm³

266.7 cm³

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the volume of a cone related to the volume of a pyramid?

A cone's volume is half that of a pyramid with the same base area and height.

A cone's volume is twice that of a pyramid with the same base area and height.

A cone's volume is the same as a pyramid with the same base area and height.

A cone's volume is one-third that of a pyramid with the same base area and height.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the formula for the volume of a sphere with radius r?

πr³

4/3 πr³

2/3 πr³

3/4 πr³

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you calculate the volume of a hemisphere with radius 11 cm?

4/3 π(11)²

1/2 × 4/3 π(11)³

4/3 π(11)³

2/3 π(11)³

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the volume of a cone with radius 3 cm and height 12 cm?

150 cm³

36π cm³

113.1 cm³

200 cm³

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a frustum?

A sphere cut in half

A pyramid with a square base

A cone with the top part removed

A cone with a circular base

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