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Answer:
The volume of radius is × π × radius³ Proved
Explanation:
Given as :
We know that volume of sphere is v = × π × radius³
Or, v = × π × r³
Let prove the volume of sphere
So, From the figure of sphere
At the height of z , there is shaded disk with radius x
Let Find the area of triangle with side x , z , r
<u>From Pythagorean theorem</u>
x² + z² = r²
Or, x² = r² - z²
Or, x =
Now, Area of shaded disk = Area = π × x²
Where x is the radius of disk
Or, Area of shaded disk = π × () ²
∴ Area of shaded disk = π × (r² - z²)
Again
<u>If we calculate the area of all horizontal disk, we can get the volume of sphere</u>
So, we simply integrate the area of all disk from - r to + r
i.e volume =
Or, v = -
Or, v = π r² (r + r) - π
Or, v = π r² (r + r) - π
Or, v = 2πr³ - π
Or, v = 2πr³ ()
Or, v = 2πr³ ×
∴ v = × π × r³
Hence, The volume of radius is × π × radius³ Proved . Answer
