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Question
The horizontal cross-section of a water tank is in the shape of a rectangle with semi-circle at one end, as shown in the following figure. The water is 2.4 metres deep in the tank. Calculate the volume of water in the tank in gallons.
Solution
Length = 21 m
Depth of water = 2.4 m
Breadth = 7 m
Therefore, radius of semicircle = `7/2 m`
Area of cross-section = Area of rectangle + Area of semicircle
= `1 xx b + 1/2pir^2`
= `21 xx 7 + 1/2 xx 22/7 xx 7/2 xx 7/2`
= `147 + 77/4`
= `(588 + 77)/4`
= `665/4 m ^2`
Therefore, volume of water filled in gallons
= `665/4 xx 2.4 m^3`
= 665 × 0.6
= 399 m3
= 399 × 1003 cm3
= `(399 xx 100 xx 100 xx 100)/1000` gallons
= `(399 xx 100 xx 100 xx 100)/(1000 xx 4.5)`
= `(399 xx 100 xx 100 xx 100 xx 10)/(1000 xx 45 )` gallons
= `1330000/15` gallons
= `266000/3` gallons
= 88666.67 gallons
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