Question

The celestial sphere shown at right has radius
9 inches. The planet in the sphere’s center
has radius 3 inches. What is the ratio of the
volume of the planet to the volume of the
celestial sphere? What is the ratio of the
surface area of the planet to the surface area
of the celestial sphere?

Answer 1

What is the formula for the volume of a sphere?

Answer 2

4/3 pi3 right

Answer 3

4/3 pi r^3

Answer 4

well find the volume of each one first
where the first volume has r=9
and the second has r=3

Why do we want the volume? Well we want to compare them right.

Answer 5

i have for r=9 is 972pi3

Answer 6

and r=3 is 36pi3

Answer 7

Looks right but Im wondering where the 3 came from :P in pi3
I think you put it in by mistake.

Answer 8

you know what ratio is right? basically a fraction and fractions is when you divide.

You have to values so you divide one value with the other and you have the ratio

Answer 9

so that mean 1:3 right?

Answer 10

is
\[\frac{972\pi}{36\pi}\]
1:3?

Answer 11

so i got 27

Answer 12

if tha's what is then yes for the volume.

Do the same for surface area.

Find the formula for surface area and use r=9 and r=3

Answer 13

324pi and 36pi