0.

Question

(07.02 MC)

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 segment AD = 4 cm, what is the smallest diameter of wrapper that will fit the candy bar? (1 point)

Triangle ABC in which point E is between points A and B, point D is between points A and C, point F is between points B and C, segments AE and EB are congruent, segments BF and FC are congruent, and angles AED, ABF, and DFC are right angles.

7 cm

8 cm

9 cm

10 cm

Answer 1

To find the smallest diameter of a cylindrical container that can fit the candy bar ABC, we first need to determine the dimensions of the triangle ABC.

From the description, we know:

• Segment AD = 4 cm, which means the height of triangle ABC from point D (the vertex opposite to the base BC) to segment BC is 4 cm.

Let’s analyze the triangle ABC further:

• Since segment AD is a height, and angles AED, ABF, and DFC are right angles, we can see that triangle ABC is divided into smaller sections through points E and F.
• AE = EB and BF = FC would imply that E and F are midpoints of their respective segments.

Since we don’t have the specific lengths of segments AB, BC, and AC directly, we can still analyze the configuration based on the right triangles created by drawing the heights from the vertices to the opposite sides.

The diameter of the cylinder that can fit the triangle is equal to the width of the triangle at its widest point. For a triangle with right angles along with the sides meeting at points A, B, C, the diameter of the cylinder can be calculated at the base BC.

Since AD = height from A to BC = 4 cm, and AE = EB, each half of the base would give us the width of segments A to E and E to B.

To fit the cylinder snugly around the triangle, we would typically calculate the diameter of the circumcircle (since the cylinder is circumscribed about the triangle).

Using the triangle's dimensions and Pythagorean theorem:

1. The potential maximum width could be calculated from the circumradius, which involves both the height and width of the triangle.

After analysis using the triangle's segments, if we consider the right angles in the shapes and given options:

• You can roughly assume that the dimensions given with segment AD suggest a maximum width that would likely fit the options given.

Among the given options:

1. 7 cm
2. 8 cm
3. 9 cm
4. 10 cm

The height indicates a larger span across the triangle, typically leading to a larger diameter. Testing options leads us towards the configurations.

To fit appropriately about AD = 4 cm, it seems plausible that the diameter fitting perfectly with the triangle's dimensions would be potentially 8 cm, while it could fit also close to 10 cm considering it needs to fully encompass.

Final Answer: 10 cm.