Question

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

​

Answer 1

Answer:

• CSA = 572cm²

Step-by-step explanation:

The diagram is as follows:

[ Refer To the attachment ]

Now, the given parameters are:

• The diameter of the hemisphere = D = 14 cm

• The radius of the hemisphere = r = 7 cm

• Also, the height of the cylinder = h = (13-7) = 6 cm

• And, the radius of the hollow hemisphere = 7 cm

Now, the inner surface area of the vessel = CSA of the cylindrical part + CSA of hemispherical part

➡ The inner surface area of the vessel = (2πrh+2πr²) cm²

➡The inner surface area of the vessel = 2πr(h+r) cm²

➡The inner surface area of the vessel = 2×(22/7)×7(6+7) cm²

➡ The inner surface area of the vessel = 572 cm².

Answer 2

To find :-

• inner surface area of the vessel

Given :-

• Diameter of hemisphere = 14cm

• Total height of vessel = 13cm

Solution :-

Radius of hemisphere r = $\dfrac{14}{2}$ = 7cm

height of cylinder h = 13 - 7 = 6cm

___________

Total inner surface area of vessel

= inner surface area of hemisphere + inner surface area of cylinder

$\: = 2\pi {r}^{2} + 2\pi \: r \: h$

$= 2\pi \times {(7)}^{2} \: + 2\pi \: \times 7 \times 6$

$= 98\pi + 84\pi = 182\pi$

$= 182 \times \dfrac{22}{7} = 572 {cm}^{2}$

Inner surface area

= $572 {cm}^{2}$