Question

A solid cylinder has total surface area of 462 sq cm.Its curved area is one third of its total surface area.Find the volume of the cylinder...

Answer 1

Volume of cylinder = ($\pi$r²h)
Total surface area of solid cylinder = 2$\pi$rh + 2$\pi$r²
Curved surface area of cylinder = 2$\pi$rh
Since we don't know the radius or the height first we have to calculate them

(462-154) = 2$\pi$r²
(308)/2$\pi$ = r²
49.02 = r²
7.0 cm = r

462/3 = 2$\pi$rh
(154)/(2$\pi$ * 7) = rh
3.5 cm = h

Volume of cylinder = $\pi$r²h
                              = $\pi$*(7)²(3.5)
                              = 539 cm³