Free Printable Calculus 7.2 MC Practice

1.

CALCULATOR: The volume of the solid formed by revolving the region bounded by the graph of $y=\left(x-3\right)^2$ and the x-axis around the x-axis is given by which of the following integrals?

a)

$\pi\int_0^3\left(x-3\right)^2dx$

b)

$\pi\int_0^3\left(x-3\right)^4dx$

c)

$2\pi\int_0^3\left(x-3\right)^2dx$

d)

$2\pi\int_0^3x\left(x-3\right)^2dx$

2.

NO CALCULATOR: Which definite integral represents a volume of a sphere with radius 2?

a)

$\pi\int_{-2}^2\left(x^2-4\right)dx$

b)

$\pi\int_{-2}^2\left(x^2+4\right)dx$

c)

$2\pi\int_0^2\left(4-x^2\right)dx$

d)

$2\pi\int_{-2}^2\left(4-x^2\right)dx$

3.

CALCULATOR: The region enclosed by the line $x+y=1$ and the coordinate axes is rotated about the line $y=-1$ . What is the exact volume of the solid that is generated?

a)

$\frac{4\pi}{3}$

b)

$\frac{17\pi}{2}$

c)

$\frac{17\pi}{4}$

d)

$\frac{2\pi}{3}$

4.

CALCULATOR: A region in the first quadrant is enclosed by the coordinate axes and the lines $y=k$ and $x=3k$ , where $k>0$ . If the volume of the solid that is generated by rotating the region about the y-axis is $72\pi$ , then k = ?

a)

$3^{\frac{1}{3}}$

b)

2

c)

3

d)

$2\sqrt{3}$

5.

CALCULATOR: The region enclosed by the x-axis, the curve $y=\arcsin x$ , and the line x = 1 is rotated about the line x = 1. What is the volume of the solid that is generated?

a)

0.178

b)

0.365

c)

0.571

d)

1.119

6.

NO CALCULATOR: The base of a solid is the region in the first quadrant bounded by the line x + 2y = 4 and the coordinate axes. What is the volume of the solid if every cross section perpendicular to the x-axis is a semicircle?

a)

$\frac{2\pi}{3}$

b)

$\frac{4\pi}{3}$

c)

$\frac{8\pi}{3}$

d)

$\frac{32\pi}{3}$

7.

NO CALCULATOR: A solid has a circular base centered at the origin with a radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, then it's volume is...?

HINT: The area of an equilateral triangle is found by using $A=\frac{s^2}{4}\sqrt[]{3}$ .

a)

36

b)

$12\sqrt{3}$

c)

$24\sqrt{3}$

d)

$36\sqrt{3}$

Calculus 7.2 MC Practice

Total questions: 7

Worksheet time: 35mins

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