Question

If the radius of a sphere is doubled, its surface area is multiplied byA. 2B. 4C. 27D. 16

Answer 1

B. 4

Explanation:

The surface area of a sphere is calculated using the formula:

`S_o=4\pi r^2\text{ where r=radius}`

If the radius is doubled:

• The new radius, R=2r

We then have the new surface area as:

`\begin{gathered} S_1=4\pi R^2=4\pi(2r)^2 \\ =4\pi(4r^2) \\ =4*4\pi r^2 \\ S_1=4* S_0 \end{gathered}`

We see from the above (4 x So) that if the radius of a sphere is doubled, its surface area is multiplied by 4.

The correct choice is B.