Is the derivative of the volume of a sphere equal to its surface area?

The rate of change of the volume of the sphere is equal to the surface area of the sphere. The outside of the paint is the new boundary of the sphere, and the inside of the paint is added to the volume. This explains why the derivative (rate of change) of the volume is the surface area (SA).

What will happen to surface area and volume of a sphere when its radius is doubled?

Just like we saw for the sphere, both surface area and volume increased when the radius doubled, and volume increased more than surface area.

How much will the volume and the surface area of a sphere be reduced if the radius of the sphere is halved?

Answer: If the radius of the sphere is reduced to it’s half, then the volume of the sphere will reduce by 8 times.

Is there a relationship between volume and surface area?

The increase in volume is always greater than the increase in surface area. For cubes smaller than this, surface area is greater relative to volume than it is in larger cubes (where volume is greater relative to surface area).

What happens to the volume of a sphere when its diameter is halved?

So if you halve the radius of a sphere, the volume of the resulting smaller sphere will be 1/8 of the volume of the original sphere.

What happens to the volume of a sphere if the radius is multiplied by 19?

The formula for the volume of a sphere is 4/3 times pi times the radius cubed. For example, if the radius of your sphere equals 19 inches, multiply 19 by 19 to get 361 square inches. Multiply the result by the radius. In this example, multiply 361 square inches by 19 inches to get 6,859 cubic inches.

What is the volume of a half sphere also called a hemisphere?

We can easily find the volume of the hemisphere since the base of the sphere is circular. The volume of the hemisphere is derived by Archimedes. The volume of a hemisphere = (2/3)πr3 cubic units.

What happens to the volume of a sphere when the radius is halved?

The volume of sphere gets one eighth when the radius is halved as, r = r/2. As, volume of sphere = (4/3)πr3 = (4/3)π(r/2)3 = (4/3)π(r3/8) = volume/8. Thus, the volume of sphere gets one eighth as soon as its radius gets halved.

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