Use the relationship among the formulas for the volumes of cones, cylinders, and spheres to solve the following problem. The volume of a cylinder is 36 cm3 . 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 point)
Responses
24 cm3
24 cm cubed
54 cm3
54 cm cubed
18 cm3
18 cm cubed
12 cm3
The relationship between the volume of a cylinder and the volume of a sphere is that the volume of the sphere is exactly two-thirds of the volume of the cylinder.
Given the volume of the cylinder is 36 cm³, the volume of the sphere would be (2/3) * 36 cm³.
Simplifying, we have (2/3) * 36 = 24 cm³.
Therefore, the volume of the sphere is 24 cm³.
Use the relationship among the formulas for the volumes of cones, cylinders, and spheres to solve the following problem. The volume of a cylinder is 36 cm3 . 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 point)
Responses
24 cm3
24 cm cubed
54 cm3
54 cm cubed
18 cm3
18 cm cubed
12 cm3
The relationship between the volume of a cylinder and the volume of a sphere is that the volume of the sphere is four-thirds of the volume of the cylinder if the height of the cylinder is equal to the diameter of the sphere.
Given the volume of the cylinder is 36 cm³, the volume of the sphere would be (4/3) * 36 cm³.
Simplifying, we have (4/3) * 36 = 48 cm³.
Therefore, the volume of the sphere is 48 cm³.
thats not an answer
Use the relationship among the formulas for the volumes of cones, cylinders, and spheres to solve the following problem. The volume of a cylinder is 36 cm3 . 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 point)
Responses
A. 24 cm3
B. 54 cm3
C. 18 cm3
D.12 cm3
To solve this problem, we need to use the relationship between the volumes of a cylinder and a sphere.
The volume of a cylinder is given by the formula Vcylinder = π * r² * h, where r is the radius and h is the height.
We are given that the volume of the cylinder is 36 cm³. Let's assume the radius of the cylinder is r and the height of the cylinder is also r (as given in the question).
Substituting these values into the formula, we have:
36 cm³ = π * r² * r
Simplifying the equation, we get:
r³ = 36 / π
Now, let's find the volume of the sphere using the formula Vsphere = (4/3) * π * r³. We can substitute the value of r³ that we found earlier:
Vsphere = (4/3) * π * (36 / π)
Simplifying further, we get:
Vsphere = (4/3) * 36
Calculating the volume:
Vsphere = 48 cm³
Therefore, the volume of the sphere is 48 cm³.
The correct answer is A. 24 cm³
The volume of a cone is 253 π cm3 . What is the volume of a sphere if its radius is the same as the cone’s and the height of the cone is equal to the sphere’s diameter?(1 point)
Responses
25 π cm3
25 pi cm cubed
252 π cm3
Start Fraction 25 over 2 End Fraction pi cm cubed
503 π cm3
Start Fraction 50 over 3 End Fraction pi cm cubed
256 π cm3
To solve this problem, we need to use the relationship between the volumes of a cone and a sphere.
The volume of a cone is given by the formula Vcone = (1/3) * π * r² * h, where r is the radius and h is the height.
We are given that the volume of the cone is 253π cm³. Let's assume the radius of the cone is r and the height of the cone is also r (as given in the question).
Substituting these values into the formula, we have:
253π = (1/3) * π * r² * r
Simplifying the equation, we get:
r³ = (253 * 3) / π
Now, let's find the volume of the sphere using the formula Vsphere = (4/3) * π * r³. We can substitute the value of r³ that we found earlier:
Vsphere = (4/3) * π * ((253 * 3) / π)
Simplifying further, we get:
Vsphere = (4/3) * 253 * 3
Calculating the volume:
Vsphere = 1012π
Therefore, the volume of the sphere is 1012π cm³.
The correct answer is not provided in the given responses.
The volume of a cone is 25/3 π cm3 . What is the volume of a sphere if its radius is the same as the cone’s and the height of the cone is equal to the sphere’s diameter?(1 point)
Responses
25 π cm3
25/2 π cm3
50/3 π cm3
25/6 π cm3
To solve this problem, we need to use the relationship between the volumes of a cone and a sphere.
The volume of a cone is given by the formula Vcone = (1/3) * π * r² * h, where r is the radius and h is the height.
We are given that the volume of the cone is 25/3π cm³. Let's assume the radius of the cone is r and the height of the cone is also r (as given in the question).
Substituting these values into the formula, we have:
25/3π = (1/3) * π * r² * r
Simplifying the equation, we get:
r³ = (25/3π) * 3/π
r³ = 25/π
Now, let's find the volume of the sphere using the formula Vsphere = (4/3) * π * r³. We can substitute the value of r³ that we found earlier:
Vsphere = (4/3) * π * (25/π)
Simplifying further, we get:
Vsphere = (4/3) * 25
Calculating the volume:
Vsphere = (100/3)π
Therefore, the volume of the sphere is (100/3)π cm³.
The correct answer is not provided in the given responses.