Question

1. what is the height of cylinder pictured below? 5 in. 13 in. 8 in 144 in 12 in 54 in

Explanation:

Step1: Identify the right triangle

The diameter of the base (5 in) and the height of the cylinder form the legs of a right triangle, with the diagonal (13 in) as the hypotenuse.

Step2: Apply Pythagorean theorem

Let \( h \) be the height. The diameter is 5 in, so the radius - related leg is 5 in? Wait, no, the diameter is 5 in, so one leg (let's say \( a = 5 \)) and the height \( h \) (leg \( b \)) and hypotenuse \( c=13 \). By Pythagorean theorem \( a^{2}+b^{2}=c^{2} \), so \( 5^{2}+h^{2}=13^{2} \).

Step3: Solve for h

\( 25 + h^{2}=169 \), then \( h^{2}=169 - 25=144 \), so \( h = \sqrt{144}=12 \) in.

Answer:

12 in (corresponding to the option "12 in")