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# A cone of height 24cm has a curved surface area 550cm2. Find it's volume

Arun
25763 Points
one year ago
Height of the cone (h) = 24 cm

Let r сm be the radius of the base and l cm be the slant height of the cone. Then,

l = root under (√r2+ h2 ) = root under (√r2 + 242) = root under (√r2 + 576)

Now, Curved surface area = πrl ⇒ 22/7 x r x root under (√r2 + 576) = 550

⇒ r root under (√r2 + 576) = 550 x 7/22 ⇒ r root under (√r2 + 576) = 175

Squaring both the sides we get

r2(r2 + 576) = 30625

(r2)2 + 576r2 - 30625 = 0

Let r2 = x

∴ x2 + 576x - 30625 = 0

x2 + 625x – 49x - 30625 = 0

x(x + 625) - 49(x + 625) = 0

(x + 625)(x - 49) = 0

x + 625 = 0, x - 49 = 0

x = - 625, x = 49

x is not equals to - 625, x = 49

∴ r2 = 49 ⇒ r = √49 ⇒ r = 7 cm

∴ Volume of the cone = 1/3πr2h = 1/3 x 22/7 x 72 x 24 = 1232 cm3