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 ad = 3 cm, what is the smallest diameter of wrapper that will fit the candy bar?

Explanation:

Step1: Use the property of perpendicular bisectors

In a triangle, the circum - radius is related to the sides. Here, \(D\) is the circum - center (since \(DE\) is the perpendicular bisector of \(AB\), \(DF\) is the perpendicular bisector of \(BC\)). For a right - angled triangle (if we assume some properties from the perpendicular bisectors and the given structure, the circum - radius \(R\) of a triangle is given by the formula \(R=\frac{AD}{1}\) (in a right - angled triangle, the circum - radius is half of the hypotenuse. Here, if we consider the triangle formed in the circum - scribing context, and given the perpendicular bisector properties, the length of \(AD\) is related to the circum - radius).
Since \(AD = 3\mathrm{cm}\), the diameter \(d\) of the circum - circle (which is the size of the wrapper) is \(d = 2R\).

Step2: Calculate the diameter

We know that \(R=AD\) (from the circum - center and right - angled triangle properties in the given geometric configuration). So, the diameter \(d\) of the circle (wrapper) is \(d = 2\times AD\).
Substitute \(AD = 3\mathrm{cm}\) into the formula: \(d=2\times3\mathrm{cm}\).

Answer:

\(6\mathrm{cm}\)