a cylinder is inscribed in a rectangular solid with a base length that is 10 inches and width that is 10 inches and a height of 16 inches. what is the radius of the cylinder?
Well, the first step is knowing what radius is. Radius is half of the diameter. (If you don't know what the diameter is, diameter is the straight line from one side of a circle, to the other)
To find the radius of the inscribed cylinder, we can use the concept of Pythagoras' theorem.
Step 1: Visualize the rectangular solid and the inscribed cylinder within it.
Step 2: Since the base of the rectangular solid has a length and width of 10 inches, we can imagine that the cylinder is inscribed in the base, with its diameter equal to the shorter length or width of the base.
Step 3: Since we have a right-angled triangle formed by the base and the height of the rectangular solid, we can apply Pythagoras' theorem to find the length of the diagonal.
- The base of the rectangular solid is 10 inches.
- The height is 16 inches.
Using the Pythagorean theorem, a^2 + b^2 = c^2, where:
- a and b are the two shorter sides of a right-angled triangle.
- c is the hypotenuse (diagonal) of the right-angled triangle.
Applying Pythagoras' theorem to our situation, we can substitute the values of a = 10 inches and b = 16 inches into the equation:
10^2 + 16^2 = c^2
100 + 256 = c^2
356 = c^2
Step 4: Take the square root of both sides of the equation to find 'c'.
√356 = √c^2
c ≈ 18.87 inches
Step 5: Since we found the diagonal length of the base, which is equal to the diameter of the inscribed cylinder, we can divide it by 2 to get the radius.
Radius ≈ 18.87 inches / 2 ≈ 9.43 inches
Therefore, the radius of the inscribed cylinder is approximately 9.43 inches.