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Question
Volume of a cone is 1232 cm3 and its height is 24 cm. Find the surface area of the cone. `( π = 22/7)`
Solution
Let the radius of the base and slant height of the cone be r cm and lcm, respectively.
Height of the cone, h = 24 cm
Volume of the cone = 1232 cm3
∴ `1/3`πr2h = 1232 cm3
∴ `1232 = 1/3 × 22/7 × r^2 × 24`
⇒ `(1232xx3xx7)/(22xx24) = r^2 ...("Multiplying both sides by" 3xx7/22xx1/24)`
⇒ r2 = 49
⇒ r = `sqrt(49)`
⇒ r = 7 cm
Now,
l2 = r2 + h2
⇒ l2 = (7)2 + (24)2
⇒ l2 = 49 + 576
⇒ l2 = 625
⇒ l = `sqrt 625`
⇒ l = 25 cm
∴ Curved Surface area of the cone = πrl
= `22/7 xx 7 xx 25`
= 550 cm2
Thus, the surface area of the cone is approximately 550 cm2.
Notes
There is a printing mistake in the textbook, the Volume of a cone is 1232 cm3 instead of 1212 cm3
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