Question

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Given :-

Curved surface area of a cone is 550 cm² and height of cone is 24 cm. What will be it's Volume ??

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Answer 1

hi dear here is the answer



given h=24cm

csa of cone=550cm^2 csa of cone=pi*r*l

pi*R*l=550

r*l=550*7/22

r*l=175

r=175/l

now we know that

l^2=r^2+h^2

l^2=(175/l)^2+24^2

576=l^2–30625/l^2

576=l^4–30625/l^2

l^4–576l^2–30625=0

then suppose x=l^2

then the eq is

x^2–576x-30625=0

x^2–625x+49x-30625=0

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

therefore x=625

l=(x)^1/2

l=25cm

r=175/25

r=7cm

volume of cone =1/3 pi*r^2*h

1/3*22/7*49*24

1232cm^3

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Answer 2

Answer:

1232 cm³

Step-by-step explanation:

Given, height of the cone (h) = 24 cm.

Slant height (l) = √r² + h²

                       = √r² + (24)²

                       = √r² + 576.

Now,

We know that CSA of a cone = πrl

550 = (22/7) * r * √r² + h²

550 * 7 = 22 * r * √r² + 576

3850/22 = r√r² + 576

175 = r√r² + 576

On Squaring both sides, we get

(175)² = (r√r² + 576)²

30625 = r² (r² + 576)

30625 = r⁴ + 576r²

r⁴ + 576r² - 30625 = 0

r⁴ + 625r² - 49r² - 30625 = 0

r²(r² + 625) - 49(r² + 625) = 0

(r² - 49)(r² + 625) = 0

r² - 49 = 0, {Neglect negative values}

r = 7 cm,

Volume of cone:

(1/3) πr²h

= (1/3) * (22/7) * (7)² * 24

= (1/3) * 22 * 7 * 24

= 3696/3

= 1232 cm³

Therefore, volume of cone = 1232 cm³

Hope it helps!