Calculus 7.2 MC Practice

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

•  $2\sqrt{3}$  

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

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

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

• $2\pi\int_0^2\left(4-x^2\right)dx$

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

 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

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?

• $\frac{2\pi}{3}$

• $\frac{4\pi}{3}$

• $\frac{8\pi}{3}$

• $\frac{32\pi}{3}$

• 36