Question

B. Based on the values in the table, what effect does changing the

radius seem to have on the surface area of the sphere? In general,
how does multiplying the radius of a sphere by a factor of x affect the
surface area of the sphere?

Answer 1

Based on the values in the table, it can be observed that changing the radius of the sphere has a direct effect on the surface area of the sphere. As the radius increases, the surface area also increases.

Explanation:

In general, multiplying the radius of a sphere by a factor of x will result in the surface area of the sphere being multiplied by a factor of x^2. This is because the surface area of a sphere is given by the formula:

Surface Area = 4πr^2

When the radius is multiplied by a factor of x, the new radius becomes xr. Substituting this into the formula, we get:

New Surface Area = 4π(xr)^2

= 4πx^2r^2

= x^2(4πr^2)

Therefore, the surface area of the sphere is multiplied by a factor of x^2 when the radius is multiplied by a factor of x. This relationship shows that the surface area increases at a faster rate than the radius.