Volume Calculation Using Double Integrals

Volume Calculation Using Double Integrals

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
5.MD.C.5B, 6.G.A.2

Standards-aligned

Created by

Emma Peterson

FREE Resource

Standards-aligned

CCSS.5.MD.C.5B
,
CCSS.6.G.A.2
The video tutorial explains how to calculate the volume of a solid bounded by an elliptical paraboloid and specific planes using a double integral. It begins by defining the region of integration and provides a graphical representation of the paraboloid. The tutorial then sets up the double integral, evaluates it with respect to X and Y, and concludes with the final volume calculation.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main objective of the problem discussed in the video?

To find the intersection points of a paraboloid with coordinate planes

To determine the height of a paraboloid

To calculate the volume of a solid bounded by a paraboloid and planes

To find the surface area of a paraboloid

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which method is used to find the volume of the solid?

Single integral

Triple integral

Double integral

Differential equations

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What shape is the region of integration in the XY plane?

Ellipse

Triangle

Circle

Rectangle

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in setting up the double integral?

Integrate with respect to y

Evaluate the antiderivative

Integrate with respect to x

Find the limits of integration

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When integrating with respect to x, what is treated as a constant?

z

y

The paraboloid equation

x

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the next step after integrating with respect to x?

Integrate with respect to y

Find the derivative

Graph the paraboloid

Evaluate the integral at the bounds for y

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of evaluating the integral at the bounds for x?

A constant value

A function of y

A function of x

Zero

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

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