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
Answer:
241 kPa
Explanation:
The ideal gas law states that:
where
p is the gas pressure
V is its volume
n is the number of moles
R is the gas constant
T is the absolute temperature of the gas
We can rewrite the equation as
For a fixed amount of gas, n is constant, so we can write
Therefore, for a gas which undergoes a transformation we have
where the labels 1 and 2 refer to the initial and final conditions of the gas.
For the sample of gas in this problem we have
So we can solve the formula for , the final pressure:
Answer:
C. To wear shoes with hard soles
Explanation:
Answer:
B . 68.7 N
Explanation:
Given in the question that;
Force = 22 N
Mass = 7.0 kg
Velocity = 4.0 m/s
Gravitational force is the weight of wooden block , calculated as mass times acceleration due to gravity.
F= m* a
F= 7 * 9.81
F= 68.67 N
F= 68.7 N