Thread: more sphere help on ratios

sphere 1 has a surface area of A_1
and has a volume of V_1
sphere 2 has a surface area of A_2
and has a volume of V_2
if the radius of sphere 2 is 3 times greater than the radius of sphere 1,
what is the ratio A_1/A_2 of the surface areas?
what is the ration V_1/V_2 of the volumes?

_ means that the number is underscored like this -->A_1

Let r be the radius of sphere 1. Then the radius of sphere 2 is 3r. The surface area of sphere 2 is


Since the surface area of sphere 1 is
,

the ratio SA1/SA2 would be
.

Now, you do the same thing with the volume. Remember that
.

ok so in volume
V_1= 4/3(pi)r^2
V_2=12(pi)r^2

so the ration would be:

v_1/v_2=4/3(pi)r^2/12(pi)r^2=1/9

^is this correct?

The formula you used for volume is not right. It's
. The r is cubed, not squared. Can you try again?

v_1/v_2=4/3(pi)r^3/36(pi)r^3=1/27

Yep, that's right!