The correct answer is:
sphere = cylinder + cone
Suppose a sphere, cylinder, and cone all share the same radius. The cylinder and cone also share the same height, which is twice the radius. Which of the following is true about the relationship between the volume formulas for the sphere, cylinder, and cone?(1 point)
Responses
cone = cylinder – sphere
cone = cylinder – sphere
cone = sphere – cylinder
cone = sphere – cylinder
cylinder = sphere – cone
cylinder = sphere – cone
sphere = cylinder + cone
5 answers
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
18 cm3
18 cm cubed
12 cm3
12 cm cubed
54 cm3
54 cm cubed
24 cm3
Responses
18 cm3
18 cm cubed
12 cm3
12 cm cubed
54 cm3
54 cm cubed
24 cm3
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Given that the volume of the cylinder is 36 cm^3, we can write the equation as:
36 = πr^2h
We also know that the height of the cylinder is equal to the diameter of the sphere, which means the height is twice the radius:
h = 2r
Substituting the value of h in terms of r in the equation, we get:
36 = πr^2(2r)
36 = 2πr^3
To find the volume of the sphere, we use the formula V = (4/3)πr^3. Comparing this formula with the equation we derived for the cylinder, we can see that the volume of the sphere is (4/3) times the volume of the cylinder.
Therefore, the volume of the sphere would be:
(4/3) * 36 = 48 cm^3
So, the correct answer is:
48 cm^3
Given that the volume of the cylinder is 36 cm^3, we can write the equation as:
36 = πr^2h
We also know that the height of the cylinder is equal to the diameter of the sphere, which means the height is twice the radius:
h = 2r
Substituting the value of h in terms of r in the equation, we get:
36 = πr^2(2r)
36 = 2πr^3
To find the volume of the sphere, we use the formula V = (4/3)πr^3. Comparing this formula with the equation we derived for the cylinder, we can see that the volume of the sphere is (4/3) times the volume of the cylinder.
Therefore, the volume of the sphere would be:
(4/3) * 36 = 48 cm^3
So, the correct answer is:
48 cm^3
THATS NOT A ANSWER
I apologize for the misconception. Let's solve the problem step by step.
We are given that the volume of the cylinder is 36 cm^3, and we need to find the volume of the sphere.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
We are told that the height of the cylinder is equal to the sphere's diameter, which means h = 2r.
Substituting the given values, the volume of the cylinder becomes:
36 = πr^2(2r)
36 = 2πr^3
To find the volume of the sphere, we can use the formula V = (4/3)πr^3. Comparing this formula with the equation we derived for the cylinder, we can see that the volume of the sphere is (2/3) times the volume of the cylinder.
Therefore, the volume of the sphere would be:
(2/3) * 36 = 24 cm^3
So, the correct answer is:
24 cm^3
We are given that the volume of the cylinder is 36 cm^3, and we need to find the volume of the sphere.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
We are told that the height of the cylinder is equal to the sphere's diameter, which means h = 2r.
Substituting the given values, the volume of the cylinder becomes:
36 = πr^2(2r)
36 = 2πr^3
To find the volume of the sphere, we can use the formula V = (4/3)πr^3. Comparing this formula with the equation we derived for the cylinder, we can see that the volume of the sphere is (2/3) times the volume of the cylinder.
Therefore, the volume of the sphere would be:
(2/3) * 36 = 24 cm^3
So, the correct answer is:
24 cm^3