In the exact terms of pieFind the volume of a sphere with a surface area of 1296pie inches squared
The surface area of a sphere is given by the formula
Surface Area = 4πr^2,
where r is the radius of the sphere.
In this case, we are given that the surface area is 1296π inches squared. So we can write the equation as:
1296π = 4πr^2.
Dividing both sides of the equation by 4π gives:
r^2 = 1296π / (4π).
Simplifying this expression, we have:
r^2 = 324.
Taking the square root of both sides, we get:
r = √324.
Since we are looking for the volume of the sphere, we can use the formula:
Volume = (4/3)πr^3.
Plugging in the value of r, we get:
Volume = (4/3)π(√324)^3.
Simplifying this expression, we have:
Volume = (4/3)π(18)^3.
Calculating this further, we get:
Volume = (4/3)π(5832).
Finally, simplifying this expression, we have:
Volume = 7776π cubic inches.