Spheres - Volume and Surface Area

The formula for the surface area of a sphere is $$4\text{π}r^2$$ , where r is the radius of the sphere.

The formula for the volume of a sphere is $$\frac{4}{3}\text{π}r^3$$ , where r is the radius of the sphere.

Using the formula $$4\text{π}r^2$$ , the surface area is $$4\text{π}(5)^2 = 100\text{π} \text{ cm}^2$$ .

Using the formula $$\frac{4}{3}\text{π}r^3$$ , the volume is $$\frac{4}{3}\text{π}(5)^3 = \frac{500}{3}\text{π} \text{ cm}^3$$ .

The surface area is $$4\text{π}(10)^2 = 400\text{π} \text{ cm}^2$$ .

The volume is $$\frac{4}{3}\text{π}(10)^3 = \frac{4000}{3}\text{π} \text{ cm}^3$$ .

If the radius is doubled, the surface area increases by a factor of 4, since it is proportional to the square of the radius.

If the radius is doubled, the volume increases by a factor of 8, since it is proportional to the cube of the radius.

The surface area of a sphere is directly proportional to the square of its radius.

The volume of a sphere is directly proportional to the cube of its radius.