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If the radii of the right cylinder and the oblique cylinder are both 5 inches, and their volumes both equal 706.5 cubic inches, what is their height in inches? Use 3.14 for pi, and enter the number only.

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Answer: Let's denote the height of the right cylinder as "h" inches and the height of the oblique cylinder as "H" inches.

The formula for the volume of a right cylinder is V = πr^2h, where "r" is the radius and "h" is the height.

Given that the radii of both cylinders are 5 inches and their volumes are both 706.5 cubic inches, we can set up two equations based on their volumes:

For the right cylinder:

V_right = π(5 inches)^2 * h inches = 706.5 cubic inches

For the oblique cylinder:

V_oblique = π(5 inches)^2 * H inches = 706.5 cubic inches

Now, we can set these two volume equations equal to each other:

π(5 inches)^2 * h inches = π(5 inches)^2 * H inches

Since both sides have the same factor π(5 inches)^2, we can cancel it out:

h inches = H inches

Therefore, the height "h" of the right cylinder is equal to the height "H" of the oblique cylinder. Since they are the same, we can find the value of their height by solving one of the volume equations:

π(5 inches)^2 * h inches = 706.5 cubic inches

Solving for "h":

h inches = 706.5 cubic inches / (π(5 inches)^2)

h inches ≈ 706.5 cubic inches / (3.14 * 25 square inches)

h inches ≈ 9 inches

So, the height of both cylinders is approximately 9 inches.

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