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

The correct answer is: 1232 cm³

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,

l² = r²+24²

l² = r²+576

l=(r²+576​)
Curved surface area = 550 cm²
πrl = 550

22​/7 × r ×  = 550

r(r²+576​) ​ = 25×7

r²(r2+576) = 25²×7²

r⁴ + 576r² − (625×49) = 0

(r²+625)(r²−49)=0

r² cannot be negative, So, r² = 49

r = 7

Volume = (1/3)​πr²h

= (1/3)​× 22/7 ​× 49 × 24

=1232 cm³
Therefore, the correct option is b)1232 cm³