Question

A rectangular sheet of dimensions 25 cm × 7 cm is rotated about its longer side. Find the volume and the whole surface area of the solid thus generated.

Answer 1

A rectangular sheet of dimensions 25 cm × 7 cm is rotated about its longer side which make a cylinder with base 25 cm and height 7 cm.

Surface area of a base = 2πr

∴ 2πr = 25 cm

⇒ `r = (25 xx 7)/(2 xx 22) = 175/44 cm`

Volume of a cylinder = πr²h

= `22/7 xx 175/44 xx 175/44 xx 7`

= `(175 xx 175)/(2 xx 44)`

= `30625/88`

= 348.011 cm³

Surface area = 2πrh

= `2 xx 22/7 xx 175/44 xx 7`

= `44/44 xx 175`

= 175 cm²