Use the image to answer the question.
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)
The volume of a cone is given by the formula V = (1/3)πr^2h, and the volume of a cylinder is given by the formula V = πr^2h.
Given that the volume of the cylinder is 90 cubic units, we can set up the equation πr^2h = 90.
Since the cones and cylinder are congruent, the volume of one cone is equal to half the volume of the cylinder, which is 45 cubic units.
The total volume of the object is the sum of the volumes of the two cones and the cylinder. So, the volume of the whole object is V = 2(1/3)πr^2h + πr^2h = (2/3)πr^2h + πr^2h = πr^2h(2/3 + 1) = πr^2h(5/3) = (5/3)(45) = 75 cubic units.
Therefore, the volume of the whole magical object is 75 cubic units.