The volume of a small sphere is 36 pie cm cubed. The volume of a large sphere is 288 cm cubed and its radius is 6 cm.
What is the similarity ratio of the radii of the two spheres?
What is the measurement of the small sphere's radius?
For a sphere,
V = 4/3 pi r^3
Is something missing in your first sentence?
To find the similarity ratio of the radii of the two spheres, we can use the formula:
(similarity ratio) = (radius of large sphere) / (radius of small sphere)
Given that the radius of the large sphere is 6 cm, we need to find the radius of the small sphere first in order to calculate the similarity ratio.
To find the radius of the small sphere, we can use the formula for volume of a sphere:
(volume of small sphere) = (4/3) * π * (radius of small sphere)^3
We are given that the volume of the small sphere is 36π cm^3. Plugging this value into the formula, we get:
36π = (4/3) * π * (radius of small sphere)^3
Simplifying the equation, we can cancel out the π on both sides:
36 = (4/3) * (radius of small sphere)^3
Now, let's solve for the radius of the small sphere:
Multiply both sides of the equation by (3/4) to isolate the term on the right side:
(3/4) * 36 = (radius of small sphere)^3
27 = (radius of small sphere)^3
Take the cube root of both sides to solve for the radius of the small sphere:
(radius of small sphere) = ∛27
(radius of small sphere) = 3 cm
Now that we know the radius of the small sphere is 3 cm, we can calculate the similarity ratio of the radii:
(similarity ratio) = (radius of large sphere) / (radius of small sphere)
(similarity ratio) = 6 cm / 3 cm
(similarity ratio) = 2
Therefore, the similarity ratio of the radii of the two spheres is 2.