Volume Of Cone

$Lateral\ surface\ area=550cm^2=\pi r\sqrt[2]{h^2+r^2}$

$h=24cm$

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$550cm^2=\pi r\sqrt[2]{\left(24cm\right)^2+r^2}$

$\left(550cm^2\right)^2=\left(\pi r\sqrt[2]{{576cm}^2+r^2}\right)^2$

$302500cm^4=\pi^2r^2(576cm^2+r^2)$

$30649.658cm^4\approx r^2\left(576cm^2+r^2\right)$

$0\approx r^4+576cm^2r^2-30649.658cm^4$

$r^2\approx49.036cm^2{||r}^2\approx-625.037cm^2$

$r\approx7cm$

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$Volume\ of\ Cone=\frac{\pi r^2h}{3}$

$V\approx\frac{\pi\left(7cm\right)^2\left(24cm\right)}{3}$

$V\approx\pi392cm^3$

$V\approx1231.5cm^3$

$V\cong1232cm^3$ )