The volume of a small circle is 10 cubic meters. Find the volume of the larger sphere in cubis meters.
To find the volume of the larger sphere, we first need to determine the radius of the small circle. The formula for the volume of a sphere is:
V = (4/3) * π * r³
where V is the volume and r is the radius of the sphere. The volume of a circle, on the other hand, is calculated using the formula:
V = π * r²
Given that the volume of the small circle is 10 cubic meters, we can set up an equation using the volume formula for a circle:
10 = π * r²
Now, let's solve for the radius of the small circle (r):
r² = 10 / π
r² ≈ 3.183
r ≈ √(3.183)
r ≈ 1.784
Now that we know the radius of the small circle (1.784), we can calculate the volume of the larger sphere using its formula:
V = (4/3) * π * R³
where R is the radius of the larger sphere.
Since the radius of the small circle and the radius of the larger sphere are related, we can use similar triangles to find the radius of the larger sphere. The radius of the larger sphere will be twice the radius of the small circle:
R = 2 * r
R ≈ 2 * 1.784
R ≈ 3.568
Now, let's calculate the volume of the larger sphere using its radius:
V = (4/3) * π * R³
V = (4/3) * π * (3.568)³
V ≈ 179.59 cubic meters
Therefore, the volume of the larger sphere is approximately 179.59 cubic meters.