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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.
Solution
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
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