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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.
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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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