please help!

If the total surface area of cone is 704cm^2 and radius of its base is 7cm. Find the volume of cone​.

Hello Guest!

$S=\pi r^2+\pi rs=\pi r(r+s)\\ s=\frac{S}{\pi r}-r=\frac{704cm^2}{\pi \cdot7cm}-7cm$

$s=25cm$

$h=\sqrt{s^2-r^2}=\sqrt{(25^2-7^2)cm^2}$

$h=24cm$

$V=\frac{1}{3}\cdot \pi r^2h=\frac{1}{3}\cdot \pi \cdot 7^2cm^2\cdot 24cm$

$V=1231.5cm^3$

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