Question

A solid cylinder has a total surface area 462 centimetres square its curved surface area is one third of the total surface area find the volume of the cylinder

Answer 1

C.S.A=1/3*T.S.A=154
C.S.A=2πrh=154
=rh=49/2
T.S.A=2πr(r+H)=462
r^2+49/2=147/2
r^2=98/2;H=7/2
volume=πr^2h=22/7* 98/2*7/2=539

Answer 2

$\huge{\mathfrak{\red{Answer}}}$

Curved surface area = total surface area / 3.

Curved surface area = 462/3 = 154.

Rest of area = 462 - 154 = 308.

$\longrightarrow$2πr^2 = 308.

$\longrightarrow$r^2 = 308 x 7 / 44 = 49.

$\longrightarrow$r = 7.

2πrh = 154.

h = 154 / 2 x 22 = 7/2.

$\longrightarrow$Volume = πr^2 h = (22/7) x (7^2) x (7/2) = 539.

$\rm Volume = 539 cm^3$