Question

The total surface area of sphere is 4πr²and total surface area of
hemisphere is 3πr².why it is 3πr²? instead 2πr²? Explain.​

Answer 1

Answer:

Given:

Radius, r = 4 cm

The curved surface area = 2πr2 square units.

The total surface area = 3πr2 square units

Substitute the value of r in the formula.

(i) CSA of the hemisphere= 2 × 3.14 × 4 × 4

CSA = 3.14 × 32

CSA = 100.48 cm2

(ii) TSA of the hemisphere = 3 × 3.14 × 4 × 4

TSA = 3.14 × 48

TSA = 150.72 cm2

Therefore, the curved and the total surface area of the hemisphere are 100.48 and 150.72 cm2, respectively.

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Answer 2

Step-by-step explanation:

Given:The total surface area of sphere is 4πr²and total surface area of hemisphere is 3πr².

To find: why it is 3πr²? instead 2πr²? Explain.

Solution:

A sphere is a closed three dimensional object and as you know that total surface area of sphere is 4πr².

1. Sphere does not have any flat surface.
2. When we cut a sphere in two equal parts,two hemispheres are formed.
3. For example;Tennis ball is a sphere,when you cut it in between you got two hemispheres and these are only having curved surfaces and area of curved surface of hemisphere is exactly half of sphere I.e. 2πr².
4. Take one hemisphere and when you cover that hemisphere (take a sheet of that radius and cover from open end); Now it have two surfaces one is flat surface and one is curved surface.
5. Total Surface Area of hemisphere=Area of curved surface+Area of flat surface
6. When you will try to find the area of flat surface you will get that it is a circle and area of circle is πr².
7. By this way TSA of hemisphere is = 2πr²+πr²=3πr²

I hope it helps you.