Question

A solid cylinder has total surface area of 462 sq cm and its curved surface area is 1/3 of its total surface area. Find the volume of the cylinder

Answer 1

Tsa of cylinder = 462cm2

2 pi rh + 2 pi r^2 = 462 cm2

pi rh + pi r^2 = 231cm2 (1)

Csa of cylinder = 1/3 462 cm2

2 pi rh = 154 cm2

pi rh = 77cm2 (2)

Substituting 2 in 1

77 + pi r2 = 231

22/7 r² = 231 - 77

r² = 154 * 7/22

r² = 49

r = 7cm

Substituting r in 2

22/7 * 7 h =77

h = 77/22

h = 3.5cm

Vol. = pi r²h

= 22/7 * 49 * 3.5

=22 * 7 * 7/2

= 11*49

= 539 cm2

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.

$\rm Volume = 539 cm^3$