Question:
A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of the canvas required in m2 is
(a) 1760
(b) 2640
(c) 3960
(d) 7920
Solution:
For conical portion
$r=52.5 \mathrm{~m}$ and $l=40 \mathrm{~m}$
Curved surface area of the conical portion
$=\pi r l$
$=\pi \times 52.5 \times 40$
$=2100 \pi \mathrm{m}^{2}$
For cylindrical portion we have
$r=52.5 \mathrm{~m}$ and $h=4 \mathrm{~m}$
Then,
Curved surface area of cylindrical portion
$=2 \pi r h$
$=2 \times \pi \times 52.5 \times 4$
$=420 \pi \mathrm{m}^{2}$
Area of canvas used for making the tent
$=(2100 m+420) \pi$
$=2520 \times \frac{22}{7}$
$=7920 \mathrm{~m}^{2}$
Hence, the correct answer is choice (d).