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Question 55
If the diameter of the base of a cone is 42 cm andits curved surface area is 2310 $$cm^2$$, then what will be its volume (in $$cm^3$$) ?
Solution
Diameter of the base of a cone = 42 cm
radius(r) = 42/2 = 21 cm
Curved surface area = 2310 $$cm^2$$
$$\pi r l = 2310$$
$$\frac{22}{7}\times 21 \times l = 2310$$
l = 35
$$l^2 = r^2 + h^2$$
$$35^2 = 21^2 + h^2$$
$$h^2 = 1225 - 441 = 784$$
h = 28 cm
Volume = $$\frac{1}{3} \pi r^2 h =Â \frac{1}{3} \times \frac{22}{7}Â 21^2 \times 28$$
= 12936Â $$cm^3$$
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