NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 12: Surface Areas & Volumes - Exercise 12.2

Question 1

Step 1: A hemisphere means "half of a sphere". Its surface has two parts:

• The curved surface area (CSA) = \(2\pi r^2\).
• The flat circular base area = \(\pi r^2\).

Step 2: When we take two identical hemispheres and join them at their bases, they form a complete sphere. But here the question says both curved parts and both bases are included in the surface area.

Step 3: Total surface area of the combination = curved surface of both hemispheres + base of both hemispheres.

• Curved surface of two hemispheres = \(2 \times 2\pi r^2 = 4\pi r^2\).
• Base area of two hemispheres = \(2 \times \pi r^2 = 2\pi r^2\).

Step 4: Add them together:

\(4\pi r^2 + 2\pi r^2 = 6\pi r^2\).

Step 5: Since the given total surface area is also \(6\pi r^2\), the statement is true.

Note: Here radius \(r\) is measured in metres (SI unit), so the surface area is in square metres (m²).