A sphere has a volume of 200m3
. What is the volume of the smallest cube that this sphere
would fit inside of? (Hint: try drawing a diagram of a side or top view of this situation)
clearly a cube with side equal to the diameter of the sphere.
So, since for a sphere,
v = pi/6 d^3, just plug in your numbers and solve for d.
To find the volume of the smallest cube that the sphere would fit inside, we need to understand that a sphere inscribed inside a cube will touch the cube's inner surface at six points.
Let's calculate the side length of the cube using the volume of the sphere. The formula for the volume of a sphere is V = (4/3) * π * r^3, where r is the radius of the sphere.
Given that the volume of the sphere is 200 m^3, we can rearrange the equation to solve for the radius (r):
200 = (4/3) * π * r^3
First, divide by (4/3) * π:
200 / ((4/3) * π) = r^3
Next, take the cube root of both sides to find the radius:
r = (200 / ((4/3) * π))^(1/3)
Now that we have the radius, we can find the diameter of the sphere:
d = 2 * r
Finally, since the sphere touches the inner surface of the cube at six points, the side length of the cube is equal to the diameter of the sphere:
s = d
Therefore, the volume of the cube is calculated using the formula V_cube = s^3.
Let's plug in the values and calculate:
r = (200 / ((4/3) * π))^(1/3)
d = 2 * r
s = d
V_cube = s^3
By following these steps, you will be able to find the volume of the smallest cube that the given sphere would fit inside.