Question

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

• A. $V=\frac{2r(2A-\pi r^2)}{2}$
• B. $V=\frac{r(2A-\pi r^3)}{2}$
• C. $V=\frac{r(A-2\pi r^2)}{2}$
• D. $V=\frac{r(A-2\pi r^3)}{2}$

Answer 1

Answer: (C)

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

Given,
$V=\pi r^{2}h$ ...(i)
$A=2\pi r^2+2\pi rh$ ...(ii)
From (ii), $2\pi rh=A-2\pi r^2$
$\Rightarrow h=\frac{A-2\pi r^2}{2\pi r}$
On putting the value of $h$ in (i), we get
$V=\pi r^2\left(\frac{A-2\pi r^2}{2\pi r}\right)$
$\Rightarrow V=\frac{r(A-2\pi r^2)}{2}$