Question

A solid iron cylinder has total surface area of 1848 sq.m. Its curved surface area is five – sixth of its total surface area. Find the radius and height of the iron cylinder.

Answer 1

T.S.A of the cylinder = 1848 sq.cm

2πr (h + r) = 1848   ...(1)

Curved surface area = `5/6` × 1848 sq.cm

2πrh = 5 × 308

2πrh = 1540 sq.m   ...(2)

Substitute the value of 2πrh in (1)

2πr (h + r) = 1848

2πrh + 2πr² = 1848

1540 + 2πr² = 1848

2πr² = 1848 – 1540

`2 xx 22/7 xx "r"^2` = 308

r² = `(308 xx 7)/(2 xx 22)` = 49

r = 7

Radius of the cylinder = 7m

2πrh = 1540

`2 xx 22/7 xx 7 xx "h"` = 1540

h = `1540/(2 xx 22)` = 35 m

Radius of the cylinder = 7 m

Height of the cylinder = 35 m