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# A cone of height 24 cm has a surface area 550 sq.cm, find its volume?

- 1323 cm
^{3} - 1232 cm
^{3} - 2321 cm
^{3} - 2123 cm
^{3}

^{3}^{3}^{3}^{3}Hint:

Curved surface area = πrl

Volume of cone= (1/3)πr2h

## The correct answer is: 1232 cm^{3}

### We have given the dimensions of cone

Height, h = 24cm

Curved surface area = 550 sq.cm

Let r cm be the radius and l cm the slant height. Then,

l^{2 }= r^{2}+24^{2}

l^{2 }= r^{2}+576

l=(r^{2}+576)

Curved surface area = 550 cm^{2}

πrl = 550

22/7 × r × = 550

r(r^{2}+576) = 25×7

r^{2}(r2+576) = 25^{2}×7^{2}

r^{4 }+ 576r^{2 }− (625×49) = 0

(r^{2}+625)(r^{2}−49)=0

r^{2 }cannot be negative, So, r^{2} = 49

r = 7

Volume = (1/3)πr^{2}h

= (1/3)× 22/7 × 49 × 24

=1232 cm^{3}

Therefore, the correct option is b)1232 cm^{3}

^{2 }= r

^{2}+24

^{2}

^{2 }= r

^{2}+576

^{2}+576)

Curved surface area = 550 cm

^{2}

πrl = 550

^{2}+576) = 25×7

^{2}(r2+576) = 25

^{2}×7

^{2}

^{4 }+ 576r

^{2 }− (625×49) = 0

^{2}+625)(r

^{2}−49)=0

^{2 }cannot be negative, So, r

^{2}= 49

^{2}h

^{3}

Therefore, the correct option is b)1232 cm

^{3}

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