Question

A milk tank is in the form of a cylinder whose radius is 1.5 m and length is 7 m . Find the quantity of milk in litres that can be stored in the tank.

Answer 1

Hint: In question it is given that radius of tank is 1.5 m and length is 7 m and capacity here is volume of tank . so, using the formula of volume of cylinder we can easily find the capacity of the tank as it is mentioned in the question that the tank is cylindrical.

Complete step by step answer:

Now, it is given that the length of the tank is 7 m and length of tank = height of cylinder.
So, we can say that height of cylindrical tank = 7 m
Now, the radius of the tank is 1.5 m.
So, radius of cylindrical tank = 1.5 m
From figure, OD = Radius of tank = 1.5 m and AB = height of tank = 7 m
Now, we know that Volume of Cylinder $=\pi {{r}^{2}}h$ , where r denotes radius of cylinder and h denotes height of cylinder and value of $\pi =3.14$ or $\pi =\dfrac{22}{7}$ .
So, volume of cylinder ABCDO $=\pi {{r}^{2}}h$……. ( i ), where r = 1.5 m and h = 7 m
So, substituting values of r = 1.5 m and h = 7 m in equation ( i ), we get
Volume of cylinder ABCDO $=\pi {{(1.5)}^{2}}(7){{m}^{3}}$
Putting $\pi =\dfrac{22}{7}$, we get
Volume of cylinder ABCDO \[=\dfrac{22}{7}\cdot {{(1.5)}^{2}}\cdot (7){{m}^{3}}\]
On solving, we get
Volume of cylinder ABCDO \[=22\cdot {{(1.5)}^{2}}{{m}^{3}}\]
On simplifying, we get
\[\text{=22 }\!\!\times\!\!\text{ 2}\text{.25}{{\text{m}}^{\text{3}}}\]
\[\text{=49}\text{.5}{{\text{m}}^{\text{3}}}\]
Now, answer is asked in litres, so we will convert metric cube into litres
Now, we know that $\text{1}{{\text{m}}^{\text{3}}}\text{=1000 litres}$
So, $\text{49}\text{.5}\times \text{1}{{\text{m}}^{\text{3}}}\text{=49}\text{.5}\times \text{1000 litres}$
On simplifying, we get
$\text{=49500 litres}$

Hence, milk tank capacity is 49500 litres.

Note: For, solving volume related problems one must know the formulas of volumes of various shapes such as cube, cuboid, sphere, frustum, cylinder etc. now, while substituting the value of $\pi $ , choose that value which will make your calculation simpler. Calculation error must be avoided and always mention the S.I unit.