To find the volume of the sphere, we need to find the radius and height of the cone first.
Since the volume of the cone is given as 253π cm^3, we can use the formula for the volume of a cone:
V = (1/3)πr^2h
where V is the volume, r is the radius, and h is the height.
Since the volume is given as 253π cm^3, we can rewrite the equation as:
253π = (1/3)πr^2h
Simplifying, we get:
r^2h = 3 * 253
r^2h = 759
Since the height of the cone is equal to the diameter of the sphere, we have:
h = 2r
Substituting this into the equation, we get:
r^2 * 2r = 759
2r^3 = 759
r^3 = 759/2
r^3 = 379.5
Taking the cube root of both sides, we find:
r ≈ 8.37
Now that we have the radius of the sphere, we can use the formula for the volume of a sphere:
V = (4/3)πr^3
Substituting r ≈ 8.37, we find:
V ≈ (4/3)π * (8.37)^3
V ≈ (4/3) * π * 593.903
V ≈ 791.609π
Therefore, the volume of the sphere is approximately 791.609π cm^3.
None of the given options perfectly match this calculation, so the closest option is "503π cm^3".
The volume of a cone is 253 π cm3. What is the volume of a sphere if its radius is the same as the cone’s and the height of the cone is equal to the sphere’s diameter?(1 point)
Responses
252 π cm3
Start Fraction 25 over 2 End Fraction pi cm cubed
25 π cm3
25 pi cm cubed
503 π cm3
Start Fraction 50 over 3 End Fraction pi cm cubed
256 π cm3
1 answer