First, we need to find the radius of the sphere. The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius. We can rearrange the formula to solve for r:
48 = (4/3)πr^3
48 * 3/4 = πr^3
36 = πr^3
r^3 = 36/π
r = (36/π)^(1/3)
Now, we can find the height of the cylinder, which is equal to the diameter of the sphere. The diameter is twice the radius, so the height of the cylinder is 2 * r.
Next, we can find the volume of the cylinder using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
V = π( (36/π)^(1/3) )^2 * 2r
V = 2π( (36/π)^(1/3) )^2r
V = 2π(36/π)^(2/3)r
Simplifying further, we get:
V = 2π(36)^(2/3)r
V = 2π(6^2)^(2/3)r
V = 2π6^(4/3)r
V = 2π6^(4/3)(36/π)^(1/3)
Therefore, the volume of the cylinder is 2π6^(4/3)(36/π)^(1/3).
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
5 answers
what does that equal
Apologies for the confusion. Let's simplify the expression further:
V = 2π6^(4/3)(36/π)^(1/3)
Since π is a constant, we can simplify further:
V = 2 * 6^(4/3) * (36/π)^(1/3)
= 2 * 6^(4/3) * (36^(1/3)) / (π^(1/3))
= 2 * 6^(4/3) * 6 / (π^(1/3))
= 12 * 6^(4/3) / (π^(1/3))
So, the volume of the cylinder is 12 * 6^(4/3) / (π^(1/3)).
V = 2π6^(4/3)(36/π)^(1/3)
Since π is a constant, we can simplify further:
V = 2 * 6^(4/3) * (36/π)^(1/3)
= 2 * 6^(4/3) * (36^(1/3)) / (π^(1/3))
= 2 * 6^(4/3) * 6 / (π^(1/3))
= 12 * 6^(4/3) / (π^(1/3))
So, the volume of the cylinder is 12 * 6^(4/3) / (π^(1/3)).
does that mean 3 cones equals 1 cylinder
No, the formula given above does not imply that 3 cones equal 1 cylinder. The formula provides the volume of a cylinder when its radius is the same as a given sphere and its height is equal to the diameter of that sphere. It is not directly related to the volume of cones or their quantity.