Question

The radius of a cylinder is 5 m more than its height. If the curved surface area of the cylinder is 792 $m^2$. What is the volume of the cylinder? (in $m^3$)

• A. 5712
• B. 5244
• C. 5544
• D. 5306
• E. 5462

Answer 1

The correct option is C 5544

Let height be 'x'm
then, Radius = (x + 5) m.
Curved surface area of cylinder = $2\pi rh$.
$792=2\times \frac{22}{7}\times (x+5)\times x\Rightarrow \frac{396\times 7}{22}=x^2+5x,126=x^2+5x,x^2+5x-126=0,x^2+14x-9x-126=0,$
x(x + 14) - 9 (x - 14) = 0,
(x-9)(x+14) = 0.
x = 9m, x =-14m
We have to take height, x = 9m because height can't be negative.
So, leaving the value of x =-14
$\therefore$ Height = 9m and radius = 9 + 5 = 14m
Hence, required volume$={\pi }^{2}rh=\frac{22}{7}\times 14\times 14\times 9=44\times 126=5544m^3$