Free Printable Volume Cross Sections AP Calculus

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Volume Cross Sections AP Calculus

Total questions: 25

Worksheet time: 3hrs 58mins

Name

Class

Date

NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the x-axis.

8π/3

32π/5

108π/5

16π/3

NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the y-axis.

8π

6π

2π

Determine the volume of the region bounded by y = x² - 2x and y = x that is rotated about y = 4.

5.4

30.6

96.133

108.332

What integral would allow you to find the volume of the region bounded by y = 2x² and y = 8 around the line y = 11.

Bounds: [0, 2]; π ∫(4x⁴ - 8)dx

Bounds: [0, 2]; π ∫((11 - 2x²)² - 9)dx

Bounds: [-2, 2]; π ∫((11 - 2x²)² - 9)dx

Bounds: [-2, 2]; π ∫(4x⁴ - 8)dx

Find the volume of the solid of revolution obtained by rotating the region in bounded by y = x³ + 1, x = 1 and y = 1 about the y-axis.

11π/3

4π/13

3π/7

2π/5

What is the volume of the solid generated by rotating the region enclosed by y = sin(x) and the x-axis, from x = 0 to x = π about the x-axis?

π²

π²/2

4π²

π/2

What is the volume of the solid formed in the second quadrant bounded by the curves y = 9 – x², the x-axis and the y-axis when it is rotated about the line x = 1?

153π/2

81π/2

648π/5

45π/2

If the region enclosed by y = 3x², y = 3 is revolved about the x-axis, what is the volume of the solid generated?

72π/5

27π/2

27π/20

9π/10

10.

Set up but do not solve an integral that will find the volume of the solid described.

11.

Set up but do not solve an integral that will find the volume of the solid described.

12.

Set up but do not solve an integral that will find the volume of the solid described.

13.

Set up but do not solve an integral that will find the volume of the solid described.

14.

15.

16.

1/2

2/3

17.

12.566

14.661

16.755

67.021

18.

32pi/5

16pi/3

16pi/5

8pi/3

19.

3pi

9pi/2

9pi

3pi/2

20.

Find the volume of the solid formed by revolving the region bounded by y = x and y = x²and the y-axis about the line y = 1.

pi/4

pi/5

pi/3

pi/2

21.

The units for Volume are always

squared

cubed

22.

23.

24.

The base of a solid is the region in the first quadrant enclosed by the parabola 𝑦 = 4𝑥² , the line 𝑥 = 1, and the 𝑥-axis. Each plane section of the solid perpendicular to the 𝑥-axis is a square. The volume of the solid is…

4/3

16/5

25.

The base of a solid is the region in the first quadrant enclosed by the graph of 𝑦 = 2 − 𝑥² and the coordinate axes. If every cross section of the solid perpendicular to the 𝑦-axis is a square, the volume of the solid is given by...

$\int_0^2\left(2-x^2\right)^2dx$

$\int_0^2\sqrt{2-y}dy$

$\int_0^2\left(2-y\right)dy$

$\int_0^2\left(2-x^2\right)dx$

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Volume Cross Sections AP Calculus

Total questions: 25

Worksheet time: 3hrs 58mins

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