Question

Given : $V=\pi r^{2}h$ and $A=2\pi r^2+2\pi rh$. Find $V$ in terms of $A,\pi$ and $r$.

• A. $V=\frac{r(A-\pi r^2)}{2}$
• B. $V=\frac{r(A-2\pi r^2)}{2}$
• C. $V=\frac{r(A+2\pi r^2)}{2}$
• D. none of these

Answer 1

Answer: (B)

$V=\frac{r(A-2\pi r^2)}{2}$

Given $A=2\pi r^{2}h+2\pi r^2$

$\Rightarrow A-2\pi r^2=2\pi rh$

$\Rightarrow h=\frac{A-2\pi r^2}{2\pi r}$

And given $V=\pi r^{2}h$

place the value$h=\frac{A-2\pi r^2}{2\pi r}$

Then $V=\pi r^2\left(\frac{A-2\pi r^2}{2\pi r}\right)$

Or $V=\frac{r(A-2\pi r^2)}{2}$