# A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 13.11. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article

**Solution:**

From the figure, it can be seen that the radius of the hemispheres scooped out is the same as the radius of the base of the cylinder since both the hemispheres are of equal radius.

Therefore, the total surface area of the article only includes the CSA of both the hemispheres and the cylinder.

TSA of the article = 2 × CSA of the hemispherical part + CSA of the cylindrical part.

We will find the TSA of the article 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 = h = 10 cm

Radius of the cylinder = radius of the hemisphere = r = 3.5 cm

TSA of the article = 2 × CSA of the hemispherical part + CSA of the cylindrical part

= 2 × 2πr^{2} + 2πrh

= 2πr (2r + h)

= 2 × 22/7 × 3.5 cm × (2 × 3.5 cm + 10 cm)

= 22 cm × 17 cm

= 374 cm^{2}

Thus, the total surface area of the article is 374 cm^{2}.

**Video Solution:**

## A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 13.11. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

### NCERT Solutions Class 10 Maths - Chapter 13 Exercise 13.1 Question 9 :

**Summary:**

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, the total surface area of the wooden article is 374 cm^{2}.