Deriving Volume of Frustums

Deriving Volume of Frustums

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to derive the volume of a frustum of a cone by setting up a coordinate system, using integration, and simplifying the resulting expressions. It begins with an introduction to the concept of a frustum, followed by the setup of a coordinate system. The tutorial then derives the volume formula through integration, expands and simplifies the integral expression, and concludes with the final formula for the frustum's volume. The video encourages viewers to verify the results using different methods.

Read more

9 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a frustum of a cone?

A cone with a curved base

A cone with its top cut off

A cone with a flat base

A cone with a hole in the center

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in deriving the volume of a frustum of a cone?

Determining the radius of the base

Finding the height of the cone

Setting up a coordinate system

Calculating the surface area

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Where is the origin placed in the coordinate system for this derivation?

At the top of the cone

At the center of the bottom circle

At the midpoint of the slant height

At the edge of the base

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What shape is formed when the region is revolved around the y-axis?

A sphere

A cylinder

A paraboloid

A frustum

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why do we need to express variables in terms of y in the integral?

To ensure the integral is with respect to y

To eliminate the constant

To simplify the calculation

To find the maximum volume

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What method is used to derive the equation of the line for eliminating x?

Trigonometric identities

Similar triangles

Coordinate geometry

Pythagorean theorem

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of substituting the expression for x into the integral?

To find the surface area

To simplify the integral

To change the variable of integration

To calculate the height

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Google

Continue with Google

Email

Continue with Email

Classlink

Continue with Classlink

Clever

Continue with Clever

or continue with

Microsoft

Microsoft

Apple

Apple

Others

Others

Already have an account?