Question

this is a cross - sectional view of candy bar abc. a candy company wants to create a cylindrical container for candy bar abc so that it is circumscribed about the candy bar. if $overline{ad}=2.5$ cm, what is the smallest diameter of wrapper that will fit the candy bar?

Explanation:

Step1: Recognize the key - length

The smallest diameter of the wrapper that will fit the candy bar is equal to the length of the diagonal of the cross - section. Here, the length of $\overline{AD}$ is given as 2.5 cm.

Step2: Recall the property of the circum - scribed circle

The diameter of the circum - scribed circle (which represents the smallest circular cross - section of the cylindrical wrapper) for a right - angled cross - section (assuming the cross - section has right angles as indicated by the perpendicular lines in the figure) is equal to the length of the hypotenuse of the right - angled triangle formed by the cross - section. In this case, the length of $\overline{AD}$ is the hypotenuse of a right - angled triangle within the cross - section.

Answer:

2.5 cm