Question

A solid cylinder has total surface area of 462 cm². Its curved surface area is one-third of
its total surface area. Find the radius and height of the cylinder.​

Answer 1

T.S.A = 462 cm²

C.S.A = 462/3 = 154cm²

T.S.A = 2πrh + 2πr²

2πrh + 2πr² = 462 cm²

154 cm² + 2πr² = 462 cm²

2πr² = 462 - 154

2πr² = 308

r² = 308/2π

r² = 308 × 1/2 × 7/22

r² = 28 × 1/2 × 7/2

r = √49

r = 7 cm

2πrh = 154

h = 154/2πr

h = 154 × 1/2 × 7/22 × 1/7

h = 7/2 cm

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.

$\rm Volume = 539 cm^3$