Use the image to answer the question.
A 3-dimensional cone is placed on top of a 3-dimensional cylinder. One of the cylinder bases is common to the cone, with the same circumference.
A 3D modeler is designing a component of a castle in a video game. She places a cone on top of a cylinder so they line up and share the same radius. The cone and the cylinder share the same height. If the volume of the cone is 50 cm3 , what is the volume of the whole object?
(1 point)
cm3
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To find the volume of the whole object, we need to add the volume of the cone and the volume of the cylinder.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the volume of the cone is 50 cm^3, we can substitute these values into the formula:
50 = (1/3)πr^2h
Since the cone and the cylinder share the same radius and height, the volume of the cylinder will also be 50 cm^3.
Therefore, the volume of the whole object is 50 + 50 = 100 cm^3.
wrong
Apologies for the incorrect response.
To find the volume of the whole object, we need to add the volume of the cone and the volume of the cylinder.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the volume of the cone is 50 cm^3, we can substitute these values into the formula:
50 = (1/3)πr^2h
Since the cone and the cylinder share the same radius and height, the volume of the cylinder will be equal to the volume of the cone.
Therefore, the volume of the whole object is 50 cm^3.
try again its not 50 or 100 or 150
Apologies for the previous incorrect responses.
To find the volume of the whole object, we need to add the volume of the cone and the volume of the cylinder.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the volume of the cone is 50 cm^3, we are given the volume of the cone.
We need to determine the volume of the cylinder. The volume of a cylinder is given by the formula V = πr^2h.
Since the cone and the cylinder share the same radius and height, the volume of the cylinder will be equal to 3 times the volume of the cone.
Therefore, the volume of the cylinder is 3 * 50 cm^3 = 150 cm^3.
To find the volume of the whole object, we add the volume of the cone and the volume of the cylinder: 50 cm^3 + 150 cm^3 = 200 cm^3.
So, the volume of the whole object is 200 cm^3.
Volume of Cones, Cylinders, and Spheres Quick Check
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Question
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
cylinder = sphere – cone
cylinder = sphere – cone
cone = sphere – cylinder
cone = sphere – cylinder
sphere = cylinder + cone
The correct answer is: sphere = cylinder + cone.
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
12 cm3
12 cm cubed
24 cm3
24 cm cubed
18 cm3
18 cm cubed
54 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 substitute these values into the formula:
36 = πr^2h
Since the height of the cylinder is equal to the sphere's diameter, the height of the cylinder is equal to 2r.
Substituting 2r for h, we have:
36 = πr^2 * 2r
Simplifying, we get:
36 = 2πr^3
Now, to solve for the volume of the sphere, we can use the relationship between the volume of a sphere and the volume of a cylinder:
Volume of sphere = (2/3) * Volume of cylinder
Substituting the volume of the cylinder (36 cm^3), we have:
Volume of sphere = (2/3) * 36
= 24 cm^3
Therefore, the volume of the sphere is 24 cm^3.
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
256 π cm3
Start Fraction 25 over 6 End Fraction pi cm cubed
252 π cm3
Start Fraction 25 over 2 End Fraction pi cm cubed
503 π cm3