Question

a milk tank is in the shape of cylinder with hemispherical of same radii attached to both ends office as shown in the figure the radius of the height of the tank is 6 metre and the radius is 1 metre calculate the maximum quantity of milk filled in the tank in litres and also calculate the total surface area of the tank ​

Answer 1

The capacity of the tank is 14660 liters approximately

The  total surface area of the tank is 31.42 m ²

Step-by-step explanation:

here , given radius = 1 m

total height of the tank = 6 m

height of the hemisphere = radius of hemisphere = 1 m

height of the cylinder =  6 - 2(1) = 6-2 = 4 m

then total capacity of the tank = volume of cylinder + volume of 2 hemisphere

= $\pi r^2h + \frac{2}{3}\pi r^3$

= $\frac{22}{7}\times 1^2 \times 4 +\frac{2}{3}\times \frac{22}{7}\times 1^3$

$\frac{22}{7} \times 4 +\frac{2}{3}\times \frac{22}{7}\\\\= \frac{88}{7} +\frac{44}{21} \\\\= 12.57 + 2.09\\\\=14.66$

hence , the capacity of the tank is 14.66 m³ = 14660 liters approximately

now, total surface area of tank = CSA  of cylinder + CSA of 2 hemisphere

= $2\pi rh+2 \pi r ^2$

= $2\pi r (r+h)$

$2\times\frac{22}{7}\times 1(1+4) \\\\= 2\times\frac{22}{7}\times 5\\\\= 31.42$

hence , the  total surface area of the tank is 31.42 m ²

#Learn more:

Two organ pipes of the same length, open at both ends produces sound of different frequencies, if their radii are different. Why?

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