Question

test prep

1. two chefs are working on cylindrical cakes. david wants to make a stripe of frosting in his cake, and he makes a cut that shows a rectangle. terri wants to put a layer of frosting in the middle of her cake, so she makes a cut that shows a circle. how was terri’s cut different from david’s?

1. name the figure that represents the two - dimensional cross section of the cylinder cut by the plane.

1. the cone is sliced horizontally, parallel to its base, as shown. choose the figure that represents the two - dimensional cross section of the cone.

a ■ c △
b ● d ○

spiral review

1. a straight path from the edge of a circular garden to the center of the garden is 7 meters long. what is the area of the garden? use 3.14 for π.

1. how many unique triangles can be made with the angle measures 48°, 64°, and 68°: none, one, or infinitely many?

Explanation:

Step 1: Answer Q8: Compare cuts

David's cut is parallel to the cylinder's height (producing a rectangle), while Terri's cut is parallel to the cylinder's circular base (producing a circle).

Step 2: Answer Q9: Identify cross-section

The plane cuts parallel to the cylinder's height, creating a rectangle.

Step 3: Answer Q10: Select cone cross-section

A horizontal cut parallel to a cone's base creates a circle, which matches option B.

Step 4: Calculate garden area (Q11)

The path is the radius $r=7$ m. Use area formula $A=\pi r^2$.
$A = 3.14 \times 7^2 = 3.14 \times 49$

Step 5: Verify triangle angles (Q12)

Sum angles: $48^\circ + 64^\circ + 68^\circ = 180^\circ$. Fixed angles mean infinitely many similar triangles.

Answer:

1. David made a cut parallel to the cylinder's vertical axis (to get a rectangle), while Terri made a cut parallel to the cylinder's circular base (to get a circle).
2. Rectangle
3. B. $\bigcirc$
4. 153.86 square meters
5. Infinitely many