Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
If the volume and curved surfaces area of a cylinder are $616 \mathrm{m}^{3}$ and $352 \mathrm{m}^{2}$ respectively, what is the total surface area of the cylinder (in $\mathrm{m}^{2}$ )
(a)429
(b)419
(c)435
(d)421
(e)417
Answer
Answer (as printed): A
Explanation
Volume of cylinder $=\pi r^{2} h$. Curved surface area of cylinder $=2 \pi r h$. $\therefore \frac{\pi r^{2} h}{2 \pi r h}=\frac{616}{352} \Rightarrow \frac{r}{2}=\frac{616}{352} \Rightarrow r=\frac{2 \times 616}{352}=3.5 \mathrm{m}$. $\therefore \pi r^{2} h=616 \Rightarrow \frac{22}{7} \times 3.5 \times 3.5 \times h=616 \Rightarrow 11 \times 3.5 \times h=616 \Rightarrow h=\frac{616}{11 \times 3.5}=16 \mathrm{m}$. $\therefore$ Total surface area of the cylinder $=2 \pi r h+2 \pi r^{2}=2 \pi r(h+r)=2 \times \frac{22}{7} \times 3.5 \times(16+3.5)=2 \times \frac{22}{7} \times 3.5 \times 19.5=22 \times 19.5=429 \text{ sq. m}$.