Question

The radius of a cylindrical milk can is half its height and its surface area is 616 sq.cms. Approximately how many litres of milk can it contain?

Given that $\surd$5 = 2.24

• A. 1.45
• B. 1.55
• C. 1.75
• D. 1.95
• E. 2.25

Answer 1

The correct option is B

1.55

It is given that r = $\frac{1}{2}$h and 2$\pi$rh + $\pi$r${}^2$= 616 cm${}^2$

$\therefore$$2\pi \times \frac{1}{2}{h}^2+\pi \times \frac{1}{4}{h}^2=616$

$\Rightarrow \frac{5}{4}\times \frac{22}{7}\times h^2=616\Rightarrow h^2=\left(616\times \frac{28}{110}\right)=\frac{28\times 28}{5}$

$\therefore$ Volume = $\pi$r${}^2$h =$\frac{22}{7}\times \frac{1}{4}{h}^2\times h=\frac{22}{7}\times \frac{1}{4}\times \frac{28\times 28}{5}\times \frac{28}{\sqrt{5}}c{m}^3$

=$\left(\frac{22\times 28\times 28}{25}\times \sqrt{5}\right)c{m}^3=\left(\frac{22\times 28\times 2.24}{25\times 1000}\right)$ litres = 1.55 litres