Question

The ratio of the radii of two spheres is 3:1. The volume of the larger sphere is 729 in3. What is the volume of the smaller sphere?

A. 81 in3
B. 54 in3
C. 243 in3
D. 27 in3

Answer 1

@terenzreignz

Answer 2

formula for volume of a sphere is
\[\Large V = \frac43\pi r^3\]

Answer 3

If the radius of the smaller sphere is r, then the radius of the larger sphere should be...?

Answer 4

3r

Answer 5

That's right...
So the volume of the larger sphere should be
\[\Large 729 = \frac43(3r)^3\]

Answer 6

where pi?

Answer 7

Sorry, forgot.
\[\Large 729 = \frac43\pi(3r)^3\]

Answer 8

Now, we're looking for the volume of the smaller sphere, which is...
\[\Large \frac{4}3\pi r^3\]

Answer 9

What we can do here is...
\[\Large 729 = \frac43\pi\cdot\color{red}{27\cdot r^3}\]
Distribute the exponent 3, and remembering that \(3^3 = 27\)

Answer 10

got it, hehe. Thanks for the logic

Answer 11

oh... good, you got it :D
I'm so sleepy now, I'm sorry I went through it so quickly.
Signing off.
-------------------
Terence out :)

Answer 12

so funny that I am interest in other's post

Answer 13

Indeed :)

Answer 14

sleep well, friend

Answer 15

Thanks @Loser66 & @terenzreignz

Answer 16

yw