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Two cones are drawn over the top and bottom of a vertically-placed cylinder. The height of the top cone from the base to the apex is h. The radius common to the cone and the cylinder is r. The height of the cylinder is h.
An animator is designing a magical object for a fantasy television series composed of two congruent cones and a cylinder. The volume of the cylinder is 90 cubic units. What is the volume of the whole object?
(1 point)
cubic units
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The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder and h is the height of the cylinder.
Given that the volume of the cylinder is 90 cubic units, we can use this information to find the radius of the cylinder.
90 = πr^2h
90 = πr^2(2h) (since the height of the cylinder is equal to the combined height of the two cones)
r^2 = 90 / (2π)
r^2 = 45 / π
r = √(45/π)
Now that we have the radius of the cylinder, we can find the volume of the whole object by adding the volumes of the two cones and the cylinder.
The volume of a cone is V = 1/3πr^2h.
Since the cones and the cylinder are congruent, the volume of the whole object would be the sum of the volumes of the two cones and the cylinder:
V = 2(1/3πr^2h) + πr^2h
V = (2/3πr^2h) + πr^2h
V = (2/3π(45/π)h) + π(45/π)h
V = (2/3)(45)h + 45h
V = 30h + 45h
V = 75h cubic units
Therefore, the volume of the whole object is 75h cubic units.