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Grade: 9

                        

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

8 months ago

Answers : (1)

Arun
25311 Points
							
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
8 months ago
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