Two spheres are used in a certain machine. One has a volume of 7 cm3 and the other has a volume of 189 cm3. The radius of the small sphere is what fraction of the radius of the large sphere?
Let the volume of the small sphere be y
And the larger one be x
y=4/3(πr³)=7.....(1)
x=4/3(πR³)=189....(2)
4/3(πr³)/(4πR²/3)=7/189
(r³/R³)=1/27
(r/R)³=(1/3)³
r/R=1/3
R=3r
That what I got when I solved for it
To find the ratio of the radii of the two spheres, we need to calculate the cube root of the ratio of their volumes.
The volume of a sphere is given by the formula V = (4/3) π r^3, where V is the volume and r is the radius.
Let's denote the radius of the small sphere as r1 and the radius of the larger sphere as r2.
We are given that the volume of the small sphere is 7 cm^3, so we have:
7 = (4/3) π r1^3
Simplifying, we find:
r1^3 = (21/(4π))
Similarly, we are given that the volume of the large sphere is 189 cm^3, so we have:
189 = (4/3) π r2^3
Simplifying, we find:
r2^3 = (567/(4π))
Now, we can find the ratio of the radii by taking the cube root of the volume ratio:
(r1/r2) = (cube root of (21/(567)))
Simplifying this, we find:
(r1/r2) ≈ 0.4
Therefore, the radius of the small sphere is approximately 0.4 times the radius of the larger sphere, or in fraction form, 2/5.