The radius of the cylinder is half its height and area of the inner part is 616 sq. cms. Approximately how… · ABC26GN4900
Subject: General Aptitude · Chapter: Volume and Surface Area
The radius of the cylinder is half its height and area of the inner part is 616 sq. cms. Approximately how many litres of milk can it contain?
(a)1.4
(b)1.53
(c)1.7
(d)1.9
(e)2.2
Answer
Explanation
It is given that $r=\frac{1}{2} h$ and $2 \pi r h+\pi r^{2}=616 \mathrm{m}^{2}$ $$\begin{aligned} & \therefore 2 \pi \times \frac{1}{2} h \times h+\pi \times \frac{1}{4} h^{2}=616 \\ & \Rightarrow \frac{5}{4} \times \frac{22}{7} \times h^{2}=616 \Rightarrow h^{2}=\left(616 \times \frac{28}{110}\right)=\frac{28 \times 28}{5} . \end{aligned}$$ ∴ Volume $$\begin{aligned} & =\pi r^{2} h=\frac{22}{7} \times \frac{1}{4} h^{2} \times h=\frac{22}{7} \times \frac{1}{4} \times \frac{28 \times 28}{5} \times \frac{28}{\sqrt{5}} \mathrm{cm}^{3} \\ & =\left(\frac{22 \times 28 \times 28}{25} \times \sqrt{5}\right) \mathrm{cm}^{3}=\left(\frac{22 \times 28 \times 28 \times 2.23}{25 \times 1000}\right) \text { litres } \\ & =1.53 \text { litres. } \end{aligned}$$
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