Search Header Logo

Calculus Revolved: Finding Volume

Authored by Lisa Lee

Mathematics

12th Grade

Calculus Revolved: Finding Volume
AI

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

    Content View

    Student View

16 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Media Image

Let the region R be the area enclosed by the function f(x)=x^2, the horizontal line y=2, and the y-axis. If the region R is the base of a solid such that each cross section perpendicular to the x-axis is a rectangle whose height is twice the length of its base in the region R, find the volume of the solid. You may use a calculator and round to the nearest thousandth.

6.034

6.098

6.077

6.048

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Media Image

Let the region R be the area enclosed by the function

f(x)=√3 and g(x)=3/2x. If the region R is the base of a solid such that each cross section perpendicular to the x-axis is an isosceles right triangle with a base in the region R, find the volume of the solid. You may use a calculator and round to the nearest thousandth.

3.35

2.89

2.40

2.65

3.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Let R be the region in the first and second quadrants above by the graph of y=20/(1+x^2) and below by the horizontal line y=2. Find the area of R. You may use a calculator and round to the nearest thousandth.

42.344

37.980

37.961

42.386

4.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Media Image

Let the region R be the area enclosed by the function f(x)=x^2-1, the horizontal line y=-4 and the vertical lines x=0 and x=4. Find the volume of the solid generated when the region R is revolved about the line y=-4. You may use a calculator and round to the nearest thousandth.

1159.619

1156.532

1160.619

1158.619

5.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Media Image

Let R be the region bounded by the graphs of y=sin (πx) and y=x^3-4x. The region R is the base of a solid and for this solid, each cross section perpendicular to the x-axis is a square. Find the volume of this solid.

9.978

9.950

9.560

0.576

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Media Image

Let R be the region bounded by the graphs of y=sin (πx) and y=x^3-4x. The region R models the surface of a small pond. At all points in R at a distance x from the y-axis, the depth of the water is given by h(x)=3-x. Find the volume of water in the pond.

9.566

9.369

8.566

8.369

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Media Image

Let the region R be the area enclosed by the function f(x)=x^2+2, the horizontal line y=2 and the vertical lines x=0 and x=4. Find the volume of the solid generated when the region R is revolved about the line y=2. You may use a calculator and round to the nearest thousandth.

645.576

643.398

648.988

647.342

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?