Question

The ratio between the radius of the base and height of the cylinder is $2:3$. If the volume is $12936c{m}^3$, what is the total surface area of the cylinder?

• A. $3080c{m}^2$
• B. $3000c{m}^2$
• C. $4000c{m}^2$
• D. $4050c{m}^2$

Answer 1

Answer: (A)

$3080c{m}^2$

Let the radius $=2x$ cm and height $=3x$ cm. Then,

Volume of cylinder $=\pi r^{2}h$

$\Rightarrow \frac{22}{7}\times (2x{)}^2\times 3x=12936$

$\Rightarrow 12x^3=\frac{12936\times 7}{22}$

$\Rightarrow x^3=\frac{12936\times 7}{12\times 22}=343$

$\Rightarrow x=7$

$\therefore$ Radius $=14cm$ and Height $=21cm$

Total surface area $=2\pi r(r+h)$

$=2\times \frac{22}{7}\times 14\times (14+21)$

$=2\times \frac{22}{7}\times 14\times 35$

$=3080c{m}^2$