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
To find the volume of the whole object, we need to add the volume of the cone and the cylinder together.
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 cone has a volume of 50 cm3, we can set up the equation:
50 = (1/3)πr^2h
Since the cone and the cylinder have the same height and radius, we can represent the radius as r and the height as h.
The volume of a cylinder is given by the formula V = πr^2h. Therefore, the volume of the cylinder in this case would be:
V_cylinder = πr^2h
To find the volume of the whole object, we add the volume of the cone and the cylinder:
V_whole object = V_cone + V_cylinder
= (1/3)πr^2h + πr^2h
= πr^2h((1/3) + 1)
= πr^2h(4/3)
= (4π/3) r^2h
Therefore, the volume of the whole object is (4π/3) r^2h. However, the specific value in cm³ cannot be determined without knowing the values of the radius and height that correspond to the cone and cylinder.