Question

A vessel is in conical shape. If its volume is $33.264$ litres and height is $72cm$, the cost of repairing its CSA at Rs.$12$ sq. m is:

• A. $5.94$
• B. $6.94$
• C. $7.95$
• D. None of the above

Answer 1

The correct option is A $5.94$

Let radius of base of vessel $=rcm$.

Given, Height of vessel $=72cm$

and Volume of vessel $=33.264$ liters $=33264c{m}^3$.

$⟹$ $\frac{1}{3}\pi r^{2}h=33264$

$⟹$ $\frac{1}{3}\times \frac{22}{7}\times r^2\times 72=33264$

$⟹$ $r^2=\frac{33264\times 3\times 7}{22\times 72}=441$

$⟹$ $r=\sqrt{441}=21cm$.

Then, slant height $l=\sqrt{r^2+h^2}$

$=\sqrt{{\left(21\right)}^2+{\left(72\right)}^2}=\sqrt{441+5184}=\sqrt{5625}$.

$\therefore l=75cm$.

Cross sectional area of conical vessel $=\pi rl$

$\therefore$ $\pi rl=\frac{22}{7}\times 21\times 75=4950c{m}^2=0.4950m^2$.

Since the cost of repairing $1m^2=Rs.12$,

therefore, cost of repairing $0.4950m^2=Rs.(0.4950\times 12)$$=Rs.5.94$.

Hence, option $A$ is correct.