Question

A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 14cm and the total height of the vessel is 13cm. Find its capacity.(Take π =22/7)

Answer 1

Hint: The vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter is given, so we can get the radius from that. The height of the vessel is also given so we can get the height of the hollow cylinder by subtracting the radius of the sphere from the height of the vessel.
Using both we will find the volume of cylinder and hemisphere we can get the capacity of the vessel by adding the volume of the cylinder and the volume of the hemisphere.

Formula used: The volume of a hemisphere with radius r is = \[\dfrac{2}{3}\pi {r^3}\]
The volume of a cylinder with radius r and height h is \[\pi {r^2}h\].

Complete step-by-step answer:
     

It is given that the vessel is in the form of a hemispherical bowl mounted by a hollow cylinder.
Also the diameter of the sphere is 14cm.
Thus the radius of the sphere is =\[\dfrac{{14}}{2} = 7cm\]
The total height of the vessel is 13cm.
We know, the height of the hemisphere is the radius of the hemisphere .So, the height of the hollow cylinder is =13cm -7cm = 6cm
For the hollow cylinder, \[r = 7cm\& h = 6cm\]
The volume of the hollow cylinder is given by the formula \[\pi {r^2}h\]
Let us substitute the values of r and h, we get,
\[ = \dfrac{{22}}{7} \times 7 \times 7 \times 6\]
\[ = 924 c{m^3}\]
For the hemisphere,
r=7 cm
The volume of the hemisphere is given by the formula \[\dfrac{2}{3}\pi {r^3}\]
Let us substitute the value of r, we get
\[ = \dfrac{2}{3} \times \dfrac{{22}}{7} \times 7 \times 7 \times 7\]
\[ = 718.66 c{m^3}\]
The capacity of the vessel = The volume of the hollow cylinder + volume of the hemisphere
\[ = \left( {924 + 718.66} \right) c{m^3}\]
\[ = 1642.66 c{m^3}\]
Hence the capacity of the vessel is \[1642.66 c{m^3}\]

Note: We should be aware that the sum of the volumes of both the shapes is the capacity of the tank. We have used the value of \[\pi \] as \[\pi = \dfrac{{22}}{7}\] .