What would the approximate diagonal through the cylinder be in inches if the radius of the cylinder is 7 inches and the height of the cylinder is 12 inches?
(4 points)
Step 1
Step 2
Step 3
Step 4
Step 1: Find the diagonal of the top of the cylinder using the radius.
The diameter of the circle at the top of the cylinder is 14 inches (2 x radius).
Now, we can find the diagonal of the circle at the top using the radius and the diameter using the Pythagorean theorem.
Diagonal = sqrt( radius^2 + (diameter/2)^2)
Diagonal = sqrt(7^2 + 7^2) = sqrt(98 + 98) = sqrt(196) = 14 inches
Step 2: Find the diagonal of the side of the cylinder using the height and the diagonal of the top.
We can treat the diagonal of the top as the hypotenuse, the radius as one leg, and half of the height as the other leg. We can again use the Pythagorean theorem to find the diagonal of the side.
Diagonal = sqrt( height^2 + radius^2)
Diagonal = sqrt(12^2 + 7^2) = sqrt(144 + 49) = sqrt(193) ≈ 13.89 inches
Step 3: Find the approximate diagonal through the cylinder.
The diagonal through the cylinder is the hypotenuse of a right triangle with the diagonal of the top and the diagonal of the side as the legs.
Diagonal = sqrt( diagonal_top^2 + diagonal_side^2)
Diagonal = sqrt(14^2 + 13.89^2) = sqrt(196 + 193.8321) = sqrt(389.8321) ≈ 19.74 inches
Therefore, the approximate diagonal through the cylinder is 19.74 inches.