Question

The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends.

Length of the cylindrical part is 7 m and radius of cylindrical part is `7/2` m.

Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.

Answer 1

Given that,

Length of cylindrical part = 7 m

Radius of cylindrical part = `7/2` m

Total surface area of figure = 2πrh + 2(2πr²)

= `2π[7/2 xx 7 + 2 xx (7/2)^2]`

= 308 m²

Volume of boiler = Volume of cylindrical part + Volume of two hemispherical parts

= `πr^2h + (4/3)πr^3`

= `π(7/2)^2 xx (7) + (4/3)π(7/2)^3`

= 269.5 + 179.66

= 449.167 m³

Required Ratio = `"Volume of cylindrical part"/"Volume of one hemispherical part"`

= `269.5/89.83`

= 3