Question

GET MEDALS!!
Mikko manufactures drinking glasses in the shape of cylinders. He wants all of the glasses to have the same fixed volume. This implies that the height of a given glass will vary inversely with the square of its diameter. One of his glasses has a diameter of 3 inches and a height of 4 inches. If another glass has a height of 9 inches, what should its diameter be?

Answer 1

Using information of the first glass to find the fix volume:
V = h*pi*r^2 = 4x pi x (3/2)^2 = 9 pi
Second glass has height = 9 inches
Same formula
V = 9 x pi x r^2
9 pi = 9 x pi x r^2 => r^2 =1 => r =1 inches
That means d=2r = 2x 1 = 2 inches

Answer 2

if when the diameter is 3 inches the height is 4 inches
so the diameter will be x when the height is 9 inches
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from this result x = (9 x 3)4 =27/4 =6,75 inches