A cone of height 24cm has a curved surface area `550c m^2dot` Find its volume. `(T a k epi=(22)/7)`

Explanation

A cone of height`=24cm`
Let the radius be `r cm`
The slant height be `l cm`.
According to condition:
`l^2=r^2+24^2`
`l^2=r^2+576`
`l=sqrt(r^2+576)`
Curved surface area`=550cm^2`
`=>pirl=550`
`=>22/7xxrxxsqrt(r^2+576)=550`
`=>rsqrt(r^2+576)=25xx7`
Squaring the both sides:
`=>r^2(r^2+576)=25^2xx7^2`
`=>r^4+576r^2−(625xx49)=0`
`=>(r^2+625)(r^2−49)=0`
`therefore r=7`
Volume`=1/3pir^2h=1/3xx22/7xx49xx24=1232 cm^3`
`therefore` Volume`=1232cm^3`