The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
The height of the cylinder is equal to the sphere's diameter, so the height of the cylinder is 2r.
The volume of the cylinder is given as 36 cm^3.
Therefore, we have 36 = πr^2(2r).
Simplifying this equation, we get 36 = 2πr^3.
Dividing both sides by 2π, we get 18 = r^3.
To find the volume of the sphere, we use the formula V = (4/3)πr^3.
Plugging in the value of r as 18, we get V = (4/3)π(18^3) = 12π(5832) = 69984π.
Approximating π as 3.14, we get 69984(3.14), which is approximately equal to 219725.76 cm^3.
The correct answer is not provided, as 219725.76 cm^3 is not one of the given choices.
Use the relationship among the formulas for the volumes of cones, cylinders, and sphere to solve the following problem. The volume of a cylinder is 36 cm^3. What is the volume of a sphere if its radius is the same as the cylinder's and the height of the cylinder is equal to the sphere's diameter?
1. 24 cm^3
2. 54 cm^3
3. 12 cm^3
4. 18 cm^3
3 answers
what's the answer bot?
I apologize for the mistake in the previous response. Let's find the correct answer.
We know that the volume of a cylinder is given by V_cylinder = πr^2h, where r is the radius and h is the height.
The height of the cylinder is given as the diameter of the sphere, so h = 2r.
We are given that the volume of the cylinder is 36 cm^3.
Therefore, we have 36 = πr^2(2r).
Simplifying this equation, we get 36 = 2πr^3.
Dividing both sides by 2π, we get 18 = r^3.
To find the volume of the sphere, we use the formula V_sphere = (4/3)πr^3.
Plugging in the value of r as 18, we get V_sphere = (4/3)π(18^3) = (4/3)π(5832) = 7776π.
Approximating π as 3.14, we get 7776(3.14), which is approximately equal to 24416.64 cm^3.
Therefore, the volume of the sphere, when the radius is the same as the cylinder's and the height of the cylinder is equal to the sphere's diameter, is approximately 24416.64 cm^3.
The closest option is "2. 54 cm^3". However, the correct answer is not provided in the given choices.
We know that the volume of a cylinder is given by V_cylinder = πr^2h, where r is the radius and h is the height.
The height of the cylinder is given as the diameter of the sphere, so h = 2r.
We are given that the volume of the cylinder is 36 cm^3.
Therefore, we have 36 = πr^2(2r).
Simplifying this equation, we get 36 = 2πr^3.
Dividing both sides by 2π, we get 18 = r^3.
To find the volume of the sphere, we use the formula V_sphere = (4/3)πr^3.
Plugging in the value of r as 18, we get V_sphere = (4/3)π(18^3) = (4/3)π(5832) = 7776π.
Approximating π as 3.14, we get 7776(3.14), which is approximately equal to 24416.64 cm^3.
Therefore, the volume of the sphere, when the radius is the same as the cylinder's and the height of the cylinder is equal to the sphere's diameter, is approximately 24416.64 cm^3.
The closest option is "2. 54 cm^3". However, the correct answer is not provided in the given choices.