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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