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Ashok Godase

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Calculus 7.2 MC Practice

Ashok Godase

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7 questions

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1. Multiple Choice
5 minutes
1 pt
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 is given by which of the following integrals?
$\pi\int_0^3\left(x-3\right)^2dx$
$\pi\int_0^3\left(x-3\right)^4dx$
$2\pi\int_0^3\left(x-3\right)^2dx$
$2\pi\int_0^3x\left(x-3\right)^2dx$
2. Multiple Choice
5 minutes
1 pt
NO CALCULATOR: Which definite integral represents a volume of a sphere with radius 2?
$\pi\int_{-2}^2\left(x^2-4\right)dx$
$\pi\int_{-2}^2\left(x^2+4\right)dx$
$2\pi\int_0^2\left(4-x^2\right)dx$
$2\pi\int_{-2}^2\left(4-x^2\right)dx$
3. Multiple Choice
5 minutes
1 pt
CALCULATOR: The region enclosed by the line $x+y=1$ and the coordinate axes is rotated about the line $y=-1$ . What is the volume of the solid that is generated?
$\frac{4\pi}{3}$
$\frac{17\pi}{2}$
$\frac{17\pi}{4}$
$\frac{2\pi}{3}$
4. Multiple Choice
5 minutes
1 pt
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 = ?
$3^{\frac{1}{3}}$
2
3
$2\sqrt{3}$
5. Multiple Choice
5 minutes
1 pt
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?
0.178
0.365
0.571
1.119
6. Multiple Choice
5 minutes
1 pt
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?
$\frac{2\pi}{3}$
$\frac{4\pi}{3}$
$\frac{8\pi}{3}$
$\frac{32\pi}{3}$
7. Multiple Choice
5 minutes
1 pt
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...?
36
$12\sqrt{3}$
$24\sqrt{3}$
$36\sqrt{3}$
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