the total surface area of sphere
Answers
Answer:
The total surface of sphere is 4πr² and total surface area of hemisphere is 3πr² instead of 2πr²? Explain.
Step-by-step explanation:
Given:
- The total surface area of sphere is 4nr²and total surface area of hemisphere is 3nr².
To find:
- why it is 3nr²? 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. 2Tr².
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 nr².
7. By this way TSA of hemisphere is = 2πr² +пr²=3пг²
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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 x 32
CSA = 100.48 cm²
(ii) TSA of the hemisphere = 3 × 3.14 × 4×4
TSA = 3.14 × 48
TSA = 150.72 cm²
CSA = 3.14 x 32
CSA = 100.48 cm²
(ii) TSA of the hemisphere = 3 × 3.14 × 4×4
TSA = 3.14 x 48
TSA = 150.72 cm²
Therefore, the curved and the total surface area of the hemisphere are 100.48 and 150.72 cm2, respectively.
I hope this answer is useful for you
