Question

A milk tank is in the shape of a with hemispheres of same radii attached to both ends of it as shown in figure. If the total height of the tank is 6 m and the radius is 1 m, calculate the maximum quantity of milk filled in the tank in litres (=22/7)

Answer 1

A milk tank is in the shape of a with hemispheres of same radii attached to both ends of it as shown in figure above .

Total tank height of the tank (H) = 6 m ,

radius (r) = 1 m

$Radius \: of \: the \: hemisphere (r) = 1\:m$

$Height \:of \: the \: cylinder (h) = H - 2r\\= 6\: m - 2\times 1 \:m \\= 6 - 2 \\= 4\: m$

$\red{ Volume \: of \: the \: milk \:tank} \\= Volume \: of \: the \: cylinder + 2( volume \: of\: hemisphere ) \\= \pi r^{2} h + 2 \times \frac{2}{3} \pi r^{3} \\= \pi r^{2} \big( h + \frac{4}{3} r \big)\\= \frac{22}{7} \times 1^{2} \big( 4 + \frac{4}{3} \times 1 \big ) \\= \frac{22}{7} \big( \frac{12+4}{3}\big) \\= \frac{22}{7} \times \frac{16}{3} \\= \frac{352}{21} \:m^{3} \\= 16.762 \times 1000\: litres \\= 16762 litres$

Therefore.,

$\red {Volume \: of \: the \: milk \:tank}$

$\green {= 16762 \:litres }$

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Answer 2

$\huge\bold\green{Question}$

A milk tank is in the shape of a with hemispheres of same radii attached to both ends of it as shown in figure. If the total height of the tank is 6 m and the radius is 1 m, calculate the maximum quantity of milk filled in the tank in litres (=22/7)

$\huge\bold\green{Answer}$

According to the question we have given :-

•°• Height of Tank (H) = 6 m

•°• Radius (r) = 1 m

So, according to the question :-

Height of Cylinder (h) = H − 2r

Now by substituting the known values

→Height of Cylinder = 6 −2 × 1

→Height of Cylinder = (6 − 2)m

→Height of Cylinder = 4 m

So, according to the question

$\begin{lgathered}\tt{ Volume_{milk \:tank}}= \tt{Volume_{cylinder} + 2( volume_{hemisphere} )} \\ \\ \implies\tt \pi r^{2} h + 2 \times \frac{2}{3} \pi r^{3} \\ \\ \implies\tt \pi r^{2} \big( h + \frac{4}{3} r \big)\\ \\ \implies\tt \frac{22}{7} \times 1^{2} \big( 4 + \frac{4}{3} \times 1 \big ) \\ \\ \implies\tt \frac{22}{7} \big( \frac{12+4}{3}\big) \\ \\ \implies \tt \frac{22}{7} \times \frac{16}{3} \\ \\ \implies\tt \frac{352}{21} \:m^{3} \\ \\ \implies\tt 16.762 \times 1000\: litres \\ \\ \implies\tt 16762 \:litres\end{lgathered}$

Hence the required volume of milk tank is 16762 ltrs.