Question

A sphere has radius 7 cm. If the radius is multiplied by 4, what is the effect on the surface area?
The surface area is multipled by 64.
The surface area is multipled by 4.
The surface area is multipled by 16.
The surface area is multipled by 2.

I got 16 and 64 for this answer. Not sure which one it is.

Answer 1

Rule: if the radius is multiplied by k, then the surface area is multiplied by k^2

Answer 2

In this case, k = 4

Answer 3

I believe it's 64. Just not sure.

Answer 4

think of a 10x10 square

it has an area of 10*10 = 100

if we multiply each side of the square by 4, what is the new area?

Answer 5

400

Answer 6

10*4 = 40 is the new side length

40*40 = 1600 is the new area

Answer 7

compare 1600 with 100

dividing the two gives 1600/100 = 16

so the new area is 16 times larger than the old area

Answer 8

Surface area of a sphere with radius r:
\(\color{#000000}{ \displaystyle A_r=4\pi r^2 }\)

Surface area of a sphere with radius kr:
\(\color{#000000}{ \displaystyle A_{rk}=4\pi (kr)^2=4\pi r^2 k^2 }\)

So, you can tell that:
\(\color{#000000}{ \displaystyle A_{rk}/A_r=\frac{4\pi r^2k^2}{4\pi r^2} =k^2 }\)

Answer 9

(Just reasoning the rule that Jim Thompson gave you)

Answer 10

I knew it had to be much larger. hence why I believed 16 or 64, I can see how it'd be 16 though.