Solve the problem.
-An oil storage tank can be described as the volume generated by revolving the area bounded by $y = \frac { 28 } { \sqrt { 49 + x ^ { 2 } } }$, $x = 0 , y = 0 , x = 2$ about the $x$-axis. Find the volume (in $\mathrm { m } ^ { 3 }$ ) of the tank.
A) $97.9 \mathrm {~m} ^ { 3 }$
B) $24.5 \mathrm {~m} ^ { 3 }$
C) $0.874 \mathrm {~m} ^ { 3 }$
D) $714 \mathrm {~m} ^ { 3 }$

Question

Quizplus · Accepted Answer

The volume of the tank can be found using the formula for the volume of a solid of revolution, specifically using the disk method. The formula is $V = \pi \int_{a}^{b} [f(x)]^2 dx$, where $f(x) = \frac{28}{\sqrt{49+x^2}}$. Substituting $f(x)$ into the formula and integrating from $x = 0$ to $x = 2$ gives the volume of the tank. The correct calculation leads to a volume of approximately $97.9 \mathrm{~m}^3$.

Solve the Problem y=2849+x2y = \frac { 28 } { \sqrt { 49 + x ^ { 2 } } }y=49+x2​28​

Solve the Problem $y = \frac { 28 } { \sqrt { 49 + x ^ { 2 } } }$