Question : The curved surface area of a right circular cone is 2310 cm$^2$ and its radius is 21 cm. If its radius is increased by 100% and height is reduced by 50%, then its capacity (in litres) will be (correct to one decimal place): (Take $\pi=\frac{22}{7}$)
Option 1: 27.8
Option 2: 28.2
Option 3: 26.7
Option 4: 25.9
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Correct Answer: 25.9
Solution :
According to the question
$\pi rl = 2310$, where $r$ = radius and $l$ = slant height.
⇒ $\frac{22}{7} \times 21 \times l = 2310$
⇒ $l = 35$
Now, for height($h$):
$l^2 = r^2 + h^2$
⇒ $35^2 = 21^2 + h^2$
⇒ $h^2 = 784$
⇒ $h = 28$
Now,
New Radius $r$ = 200% of 21 = 42
New Height $h$ = 50% of 28 = 14
New volume = $\frac{1}{3}\times\pi \times 42^2\times14$
= $\frac{1}{3}\times \frac{22}{7} \times 42 \times 42 \times 14$
= $25872$ cm$^3$
= $\frac{25872}{1000}$ litres
= 25.872 litres = 25.9 litres (approx.)
Hence, the correct answer is 25.9.
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