Question

the radius and height of a cylinder are in the ratio 7 : 2 if the volume of the cylinder is 8316 cm cube find the total surface area of the cylinder

Answer 1

VOLUME OF CYLINDER = pi X r^2 X h

Let the height be 2x
Radius = 7x

Volume = pi X 49x^2 X 2x = 3.14 X 98x^3 = 8316

x^3 = 8316 / 3.14*98 = 27.024567 cm

x = 3 cm

HEIGHT = 6 cm Radius = 21 cm

FORMULA FOR TOTAL SURFACE AREA = 2pirh + 2pir^2

= 2pir ( r + h)

= 2 X 3.14 X 21 X 27 = 3560.76 cm^2

Answer 2

let the height be 2x
and radius be 7x
therefore
the volume of cylinder =πr^2h
8316=22/7*7x^2*2x
8316=154x^2*2x
8316=308x^3
or x^3=8316/308
x^3=27
x=3
radius =3*7=21cm
height,=3*2=6cm
therefore
total surface area of cylinder =2πr(r+h)
=2*22/7*21(21+6)cm^2
=132*27cm^2
=3564cm2