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.  

 

Answer 1

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