Question

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?
step 1 ________________
step 2 ________________
step 3 ________________
step 4- answer _______________

double the radius to get the diameter = 14 in
use the Pythagorean theorem with the height 12 in and the diameter 14 in -12^2+14^2=d^2
simplify to get; d^2=340
answer -d might equal 18.4
use the Pythagorean theorem with the height 12 in and the radius 7 in -12^2+7^2=d^2
simplify to get; d^2=193
answer -d=96.5
answer -d=170
square the radius to get the diameter = 49 in
use the Pythagorean theorem with the height 12in and the diameter 49 in - 12^2+49^2=d^2
simplify the equation to get d^2=2545
answer -d might equal 50.4

Answer 1

To find the approximate diagonal through the cylinder (the length of the diagonal from the base to the top edge), we can use the Pythagorean theorem. We'll consider the diagonal as the hypotenuse of a right triangle formed by the height of the cylinder and the diameter of its base. Here's a step-by-step outline:

### Step 1
Calculate the diameter of the cylinder:
\[
\text{Diameter} = 2 \times \text{Radius} = 2 \times 7 \, \text{inches} = 14 \, \text{inches}
\]

### Step 2
Use the Pythagorean theorem to relate the height and the diameter:
\[
d^2 = (\text{Height})^2 + (\text{Diameter})^2
\]
\[
d^2 = (12 \, \text{inches})^2 + (14 \, \text{inches})^2
\]

### Step 3
Calculate the squares:
\[
d^2 = 144 + 196
\]

### Step 4 - Answer
Add the squares and take the square root:
\[
d^2 = 340
\]
\[
d = \sqrt{340} \approx 18.44 \, \text{inches}
\]

Thus, the approximate diagonal through the cylinder is **18.44 inches**.