The volume of a cylinder is calculated using the formula V = πr^2h, where r is the radius and h is the height.
Since the radius of the cylinder is the same as the sphere's, let's denote it as r.
The height of the cylinder is equal to the sphere's diameter, which is twice the radius. Therefore, the height of the cylinder is 2r.
Substituting these values into the formula, we get V = πr^2(2r).
Simplifying, V = 2πr^3.
However, we are given the volume of the sphere, not the volume of the cylinder. Therefore, we need to find r first by using the formula for the volume of a sphere, V = (4/3)πr^3.
48 = (4/3)πr^3
Multiplying both sides by (3/4) and then dividing both sides by π, we get:
r^3 = (3/4)(48/π)
r^3 = 36/π
Taking the cube root of both sides, we find r ≈ 2.2206 m.
Now we can substitute r into the formula for the volume of the cylinder:
V = 2π(2.2206^3)
V ≈ 2π(10.998)
V ≈ 21.996π
Therefore, the volume of the cylinder is approximately 21.996π m^3.
The volume of a sphere is 48 m3 . What is the volume of a cylinder if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter?(1 point)
3 answers
wrong
I apologize for the mistake. Let's try again.
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.
Given that the volume of the sphere is 48 m^3, we can set up the equation as follows:
48 = (4/3)πr^3
To find the radius, we need to isolate r. Let's start by multiplying both sides by (3/4) to get:
(3/4)(48) = πr^3
36 = πr^3
Now, divide both sides by π to solve for r^3:
r^3 = 36/π
Taking the cube root of both sides, we get:
r ≈ 2.8704 m
Now we have the radius of the sphere, which is also the radius of the cylinder.
The height of the cylinder is equal to the sphere's diameter, which is twice the radius. Therefore, the height of the cylinder is 2r = 2(2.8704) ≈ 5.7408 m.
To find the volume of the cylinder, we can use the formula V = πr^2h:
V = π(2.8704)^2(5.7408)
V ≈ 120.32π m^3
Therefore, the volume of the cylinder is approximately 120.32π m^3.
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.
Given that the volume of the sphere is 48 m^3, we can set up the equation as follows:
48 = (4/3)πr^3
To find the radius, we need to isolate r. Let's start by multiplying both sides by (3/4) to get:
(3/4)(48) = πr^3
36 = πr^3
Now, divide both sides by π to solve for r^3:
r^3 = 36/π
Taking the cube root of both sides, we get:
r ≈ 2.8704 m
Now we have the radius of the sphere, which is also the radius of the cylinder.
The height of the cylinder is equal to the sphere's diameter, which is twice the radius. Therefore, the height of the cylinder is 2r = 2(2.8704) ≈ 5.7408 m.
To find the volume of the cylinder, we can use the formula V = πr^2h:
V = π(2.8704)^2(5.7408)
V ≈ 120.32π m^3
Therefore, the volume of the cylinder is approximately 120.32π m^3.