The voulme of a shere is 72m^3. what is the voulume of a cone if its rDUIS IS THE SAME AS THE SPHERE AND ITS hight is equal to the sphere diameter?
if the sphere has radius r, then
the cone has radius r and height 2r
that means that the ratio of the cone's volume to the sphere's is
(1/3 πr^2*2r)/(4/3 πr^3) = 1/2
so the cone's volume is 1/2 * 72 = 36
You are correct. Thank you for pointing out the error in my previous explanation.
Given that the ratio of the cone's volume to the sphere's volume is 1/2, we can calculate the volume of the cone as:
Volume of cone = (1/2) * 72m^3 = 36m^3
Therefore, the volume of the cone is 36m^3. Thank you for the correction.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
Given that the volume of the sphere is 72m^3, we can solve for the radius of the sphere:
72 = (4/3)πr^3
72 = (4/3)(3.14159)(r^3)
72 = 4.18879r^3
r^3 = 72 / 4.18879
r^3 = 17.1867
r = ∛(17.1867)
r ≈ 2.65m
Now, the volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the cone and h is the height of the cone.
Since the cone has the same radius as the sphere and the height is equal to the diameter (2r), we have:
r = 2.65m
h = 2r = 2(2.65) = 5.3m
Now, we can calculate the volume of the cone:
V = (1/3)π(2.65)^2(5.3)
V = (1/3)(3.14159)(7.0225)(5.3)
V = (1/3)(3.14159)(37.16925)
V ≈ 39.2m^3
Therefore, the volume of the cone is approximately 39.2m^3.