Question

can anyone explain this thoroughly ?

Answer 1

i think i can

Answer 2

first either we need a variable for the radius of the sphere, or else we can give it a number
your choice, it makes no difference

Answer 3

r?

Answer 4

ok that is a good choice

Answer 5

if the radius of the sphere is \(r\) do you know the volume of the sphere (in terms of \(r\)?)

Answer 6

i have no idea

Answer 7

ok then i will tell you although a quick google search gives it instantly it is \[A=\frac{4}{3}\pi r^3\]

Answer 8

if the radius of the sphere is \(r\) then the length of the side of the cube is evidently \(2r\)
what is the volume of the cube?

Answer 9

a^3?

Answer 10

yeah but \(a=2r\)

Answer 11

8r^3?

Answer 12

so \[(2r)^3=8r^2\] is volume of the cube right

Answer 13

then divide and you are done
the \(r^3\) will cancel when you do that

Answer 14

i'm so confused :/

Answer 15

they want the ratio of the volumes right?

Answer 16

yes

Answer 17

the cube has volume \(8r^3\) and the sphere has volume \(\frac{4}{3}\pi r^3\)

Answer 18

the ratio is
\[\huge \frac{8r^3}{\frac{4}{3}\pi r^3}\]

Answer 19

cancel the \(r^3\) and simplify the compound fraction

Answer 20

6/pi ?