Question

4.8 surface area and volume of spheres
julie thinks that if you double the radius of a sphere, the surface area will double. is she correct? explain your reasoning.

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a sphere is $A = 4\pi r^{2}$, where $r$ is the radius.

Step2: Find new surface area when radius is doubled

If the radius is doubled ($r'=2r$), then the new surface area $A'=4\pi(2r)^{2}=4\pi\times4r^{2}=16\pi r^{2}$.

Step3: Compare original and new surface areas

The original area is $A = 4\pi r^{2}$, and the new area $A' = 16\pi r^{2}$. The ratio $\frac{A'}{A}=\frac{16\pi r^{2}}{4\pi r^{2}} = 4$.

Answer:

No, she is not correct. When the radius of a sphere is doubled, the surface area becomes 4 times the original, not 2 times, as shown by the surface - area formula $A = 4\pi r^{2}$.