Question

40. 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

SOLUTION:-

Given:

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder.

⚫The diameter of the hemisphere =14cm

So,

We know that Radius= d/2;

=) 14/2

=) Radius=7cm

⚫The total height of the vessel is 13cm

⚫Height of the cylindrical part (h):

=) 13cm -7cm

=) 6cm

Now,

The inner surface area of the vessel is;

Curved surface area of hemisphere + curved surface area of cylinder.

Using Formula

=) 2πr² + 2πrh

Inner surface area of vessel:

$(2 \times \frac{22}{7} \times 7 \times 7) + (2 \times \frac{22}{7} \times 7 \times 6) \\ \\ = > (44 \times 7) + (44 \times 6) \\ \\ = > 44(6 + 7) \: \: \: \: \: [common \: 44]\\ \\ = > 44 \times 13 \\ \\ = >572 {cm}^{2}$

So,

572cm² is the required area of inner surface area of the vessel.

Hope it helps ☺️

Answer 2

The diagram is as follows:

• Figure provided in the above 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

=> (2πrh+2πr²) cm² = 2πr(h+r) cm²

=> 2 × 22/7 × 7 (6+7) cm2 = 572 cm²