ABC26GN4948 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
If a right circular cone of height 24 cm has a volume of $1232 \mathrm{cm}^{3}$, then the area of its curved surface is
(a)$154 \mathrm{cm}^{2}$
(b)$550 \mathrm{cm}^{2}$
(c)$704 \mathrm{cm}^{2}$
(d)$1254 \mathrm{cm}^{2}$
Answer
Explanation
$\frac{1}{3} \times \frac{22}{7} \times r^{2} \times 24=1232 \Leftrightarrow r^{2}=\left(\frac{1232 \times 7 \times 3}{22 \times 24}\right)=49$ $$\Leftrightarrow r=7 .$$ Now, $r=7 \mathrm{cm}, h=24 \mathrm{cm}$. So, $l=\sqrt{(7)^{2}+(24)^{2}}=25 \mathrm{cm}$. $$\text { ∴ Curved surface area }=\left(\frac{22}{7} \times 7 \times 25\right) \mathrm{cm}^{2}=550 \mathrm{cm}^{2} .$$
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