# Thread: more sphere help on ratios

1. ## 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

2. Let r be the radius of sphere 1. Then the radius of sphere 2 is 3r. The surface area of sphere 2 is
$\displaystyle SA_2 = 4 \pi (3r)^2 = 36 \pi r^2$

Since the surface area of sphere 1 is
$\displaystyle SA_1 = 4 \pi r^2$,

the ratio SA1/SA2 would be
$\displaystyle \dfrac{SA_1}{SA_2} = \dfrac{4\pi r^2}{36\pi r^2} = \dfrac{1}{9}$.

Now, you do the same thing with the volume. Remember that
$\displaystyle V = \frac{4}{3}\pi r^3$.

3. 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?

4. The formula you used for volume is not right. It's
$\displaystyle V = \frac{4}{3}\pi r^{\bold{3}}$. The r is cubed, not squared. Can you try again?

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

6. Yep, that's right!