B

9000100001

Level: 
B
The function \(f(x) = 3 - 2x\) is graphed in the picture. Consider the region between the graph of the function on the interval \([ 0,\, 1.5] \) and the axes. Determine the solid of revolution obtained by revolving this region about \(y\)-axis
A cone with the base of radius \(1.5\).
A cone with the base of radius \(3\).
A pyramid of the height \(1.5\).
A pyramid of the height \(3\).

9000100003

Level: 
B
The function \(f(x) = x^{2} + 2\) is graphed in the picture. Consider the region between the graph of the function on the interval \([ 0,\, 1] \), both axes and the line \(x = 1\). Find the formula for the volume of the solid of revolution obtained by revolving this region about \(y\)-axis.
\(V =\pi \int _{ 0}^{3}1\, \mathrm{d}y -\pi \int _{2}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y\)
\(V =\pi \int _{ 0}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y\)
\(V =\pi \int _{ 2}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y -\pi \int _{0}^{3}1\, \mathrm{d}y\)
\(V =\pi \int _{ 2}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y\)

9000100006

Level: 
B
The function \(f(x)= \sqrt{x}\) is graphed in the picture. Consider the region bounded by the graph of \(f\) on \([ 1,\, 4] \), lines \(x = 1\), \(x = 4\) and the \(x\)-axis. Identify the formula for volume of the solid of revolution obtained by revolving this region about the \(x\)-axis.
\(V =\pi \int _{ 1}^{4}x\, \mathrm{d}x\)
\(V =\int _{ 1}^{4}x\, \mathrm{d}x\)
\(V =\pi \int _{ 1}^{4}\sqrt{x}\, \mathrm{d}x\)
\(V =\int _{ 1}^{4}\sqrt{x}\, \mathrm{d}x\)

9000100007

Level: 
B
The function \(f(x)= \sqrt{x}\) is graphed in the picture. Consider the region bounded by the graph of \(f\) on \([ 1,\, 4] \), lines \(x = 1\), \(x = 4\) and the \(x\)-axis. Find the volume of the solid of revolution obtained by revolving this region about the \(x\)-axis.
\(\frac{15} {2} \pi \)
\(\frac{17} {2} \pi \)
\(\frac{17} {2} \pi ^{2}\)
\(\frac{15} {2} \pi ^{2}\)