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?
its 200
Whats is the answer bot because its wrong
To find the volume of the whole object, we need to add the volumes of the cone and the cylinder.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
From the information given, we know that the volume of the cone is 50 cm³. Let's assume the radius and height of both the cone and the cylinder are denoted by r and h.
So, the volume of the cone would be:
50 = (1/3)πr²h
To find the volume of the whole object, we also need to calculate the volume of the cylinder.
The formula for the volume of a cylinder is V = πr^2h.
Since the cone and cylinder have the same radius and height, the volume of the cylinder would also be:
V = πr²h
Now, to find the volume of the whole object, we need to add the volumes of the cone and the cylinder:
Volume of the whole object = Volume of cone + Volume of cylinder
= 50 + πr²h
Therefore, the volume of the whole object is 50 + πr²h cm³.
We know that the volume of a cone is given by the formula 1/3 * π * r^2 * h, where r is the radius and h is the height of the cone.
Let's assume the radius of both the cone and the cylinder is r and the height is h. Since the cone and the cylinder share the same radius and height, we can calculate the volume of the whole object by adding the volumes of the cone and the cylinder.
The volume of the cone is given as 50 cm3. Let's substitute these values into the formula for the volume of the cone:
1/3 * π * r^2 * h = 50
To find the volume of the whole object, we need to add the volume of the cylinder to the volume of the cone. The volume of a cylinder is given by the formula π * r^2 * h.
So the volume of the whole object is:
V = (1/3 * π * r^2 * h) + (π * r^2 * h)
= π * r^2 * h * (1/3 + 1)
= π * r^2 * h * 4/3
Therefore, the volume of the whole object is 4/3 times the volume of the cone.
Volume of the whole object = 4/3 * 50 cm3
= 200/3 cm3
≈ 66.67 cm3
So, the volume of the whole object is approximately 66.67 cm3.