Question

a solid cylinder has total surface area of 462 cm2 . if total surface area of the cylinder is thrice of its curved surface area. then the volume of the cylinder is:

Answer 1

TSA = 462

2×22/7× r(r+h) = 462

r(r+h) = 147/2

TSA= 3× CSA

462= 3× 2×22/7× rh

42= 3× 2×2/7 ×rh

rh = 49/2

r2 + rh = 147/2

r2 = 147/2 - 49/2

r2 = 49

r = 7

vol = 22/7 × r2×h

22/7×r×rh

= 22/7 ×7×49/2

= 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.

$\rm Volume = 539 cm^3$