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Find the diagonal c in the cylinder. (Height is 10, and the diameter is 5)
To find the diagonal c in the cylinder, we need to find the length of the diagonal of the cross-section of the cylinder.
The cross-section of the cylinder is a circle with a diameter of 5 units. The diagonal of a circle is the diameter.
The diameter of the cross-section is 5 units.
Now, let's use the height of the cylinder to find the diagonal of the cylinder.
The diagonal of the cylinder can be found using the Pythagorean theorem.
In this case, the height of the cylinder is the height of the right triangle, and the diagonal of the cross-section is the hypotenuse of the right triangle.
The formula for the diagonal of a right triangle is:
c² = a² + b²
Where c is the hypotenuse (diagonal) and a and b are the legs of the right triangle.
In this case, a is the height of the cylinder (10 units) and b is the radius of the cross-section (half of the diameter, which is 2.5 units).
Plugging in the values:
c² = 10² + 2.5²
c² = 100 + 6.25
c² = 106.25
Taking the square root of both sides to solve for c:
c = √106.25
c ≈ 10.31