The volume of the circumscribed cylinder is 2154.04π cm^3. Find the radius of the sphere…show all work and steps
I need help :c
The volume of a cylinder is given by V = πr^2h, where r is the radius of the cylinder and h is the height.
The volume of a sphere is given by V = (4/3)πr^3, where r is the radius of the sphere.
We can set the two equations equal to each other and solve for r:
2154.04π = (4/3)πr^3
r^3 = (2154.04/4)
r = (2154.04/4)^(1/3)
r = 6.7 cm
Is this correct??
No, the question needs to be clarifies.
Does the sphere fit perfectly into a cylinder?
I will assume that is what you meant by "circumscribed cylinder"
Let the radius of the sphere be r, it will also be the radius of the cylinder
The cylinder must have a height of 2r , (your sketch will show that)
volume of cylinder = π r^2 h = 2π r^3 in our case
πr^3 = 2154.04
r^3 = 685.65....
r = 8.818 cm
Don't know why the robot tutor even brought up the volume of the sphere.
typo correction, about 2/3 of the way down in my solution I have
volume of cylinder = π r^2 h = 2π r^3 in our case
but then dropped that 2, so we should have
vol= 2π r^3 = 2154.04
r^3 = 343 if we use π as 3.14
r = 7
To find the radius of the sphere, we need to use the equation for the volume of a circumscribed cylinder.
The volume of a cylinder is given by the formula:
Vcylinder = πr^2h
Where:
Vcylinder = Volume of the cylinder
r = Radius of the cylinder's base
h = Height of the cylinder
In this case, we are given the volume Vcylinder = 2154.04π cm^3.
To solve for the radius of the sphere, we need to find the value of r. However, we are missing the height of the cylinder (h). Without the height, we cannot directly calculate the radius.
Please provide the height of the cylinder so we can proceed with the steps to find the radius of the sphere.