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Question 13
The radius and the height of a right circular cone are in the ratio 5 : 12. Its curved surface area is 816.4 $$cm^2$$, What is the volume (in $$cm^3$$) of the cone? (Take $$\pi = 3.14$$)
Solution
Let the radius and height e 5x and 12x.
$$l^2 = (5x)^2 + (12)^2$$
$$l^2 = 169x^2$$
l = 13x cm
Curved surface area = 816.4 $$cm^2$$
$$\pi r l =Â 816.4$$
$$3.14 \times 5x \times 13x =Â 816.4$$
x = 2
r = $$5 \times 2 = 10 cm$$
h = $$12 \times 2 = 24 cm$$
Volume of the cone = $$\frac{1}{3} \times \pi r^2 h =Â \frac{1}{3} \times 3.14 \times (10)^2 \times 24$$
= 2512 cm$$^2$$
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