Question

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2.Find the volumne of the cylinder if it's total surface area is 616cm^2.​

Answer 1

Curved S.A= 1/2 ×616=308cm 2

Total SA=616 cm 2

Curved area =2πrh=308

Total area =2πrh+2πr 2 =616

2πr 2=616−308=308

r= √308×7/2×22 =7cm

2πrh=308

h= 308×7/2×22×7

h=7cm

Answer 2

Answer:

$1077.56628018 cm^2$

Step-by-step explanation:

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2

curved surface area of cylinder = $2\pi r h$

total surface area of a right circular cylinder = $2\pi r h + 2\pi r^2$

$\frac{2\pi r h}{2\pi r h + 2\pi r^2} = \frac{1}{2}$

$\frac{ h}{ h + r} = \frac{1}{2}$

$h = r$

$2\pi r h + 2\pi r^2 = 616$

$rh + r^2 = 98$

$2r^2 = 98$

$r = h = 7$

Volume of cylinder =   $\pi r^2 h$

Volume of cylinder =   $\pi r^2 h$ = 1077.56628018 $cm^2$