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.