# 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

**Solution:**

Let's create a figure of the vessel according to the given description.

From the figure it’s clear that the inner surface area of the vessel includes the curved surface area CSA of the hemisphere and the cylinder.

Inner surface area of the vessel = CSA of the hemisphere + CSA of the cylinder

We will find the area of the vessel by using formulae;

CSA of the hemisphere = 2πr^{2}, where r is the radius of the hemisphere.

CSA of the cylinder = 2πrh

where r and h are the radius and height of the cylinder respectively.

Height of the cylinder = Total height of the vessel - height of the hemisphere.

Diameter of the hemisphere, d = 14 cm

Radius of the hemisphere, r = 14/2 cm = 7 cm

Height of the hemisphere = radius of the hemisphere, r = 7cm

Radius of the cylinder, r = 7 cm

Height of the cylinder = Total height of the vessel - height of the hemisphere

h = 13 cm - 7 cm = 6 cm

Inner surface area of the vessel = CSA of the hemisphere + CSA of the cylinder

= 2πr^{2} + 2πrh

= 2πr (r + h)

= 2 × 22/7 × 7cm (7 cm + 6 cm)

= 2 × 22 × 13 cm^{2}

= 572 cm^{2}

Thus, the inner surface area of the vessel is 572 cm^{2}.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 13

**Video Solution:**

## 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

NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.1 Question 2

**Summary:**

If a vessel is in the form of a hollow hemisphere mounted by a hollow cylinder and the diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm, the inner surface area of the vessel is 572 cm^{2}.

**☛ Related Questions:**

- A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
- A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
- A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
- A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 13.10). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

visual curriculum