Mensuration Ques 32
Question
The ratio between curved surface area and total surface area of a circular cylinder is $3: 5$. If the curved surface area is $1848 cm^{2}$, what is the height of the cylinder? (in cm.)
(1) 28
(2) 14
(3) 17
(4) 21
(5) 7
(IBPS RRBs Officers CWE (Prelim Exam) 09.09.2017 IInd Sitting)
Show Answer
Correct Answer: (4)
Solution: (4)
Curved surface area of cylinder $=2 \pi r h$
Total surface area of cylinder $=2 \pi r h+2 \pi r^{2}=2 \pi r(h+r)$
According to the question,
$\frac{2 \pi r h}{2 \pi r(h+r)}=\frac{3}{5}$
$\Rightarrow 3 h+3 r=5 h$
$\Rightarrow 2 h=3 r$
$\therefore 2 \pi r h=1848$
$\Rightarrow 2 \times \frac{22}{7} \times \frac{2}{3} \times h^{2}=1848$
$\Rightarrow h^{2}=\frac{1848 \times 7 \times 3}{22 \times 4}=441$
$\Rightarrow h=\sqrt{441}=21 cm$.
BETA
