Question

1. anthony measured a can of campbells soup. suppose the can is a cylinder and has a height of 6 inches and a diameter of 10.8 inches. which measurement is closest to the total surface area of the can in square inches? a) 685 b) 387 c) 1140 d) 887 13. name the solid that would be formed by rotating the shape about a given axis. a) frustum b) sphere c) cylinder d) cone which of the following shows a triangle cross - section? a) b)

Explanation:

Step1: Calculate the radius

The diameter $d = 10.8$ inches, so the radius $r=\frac{d}{2}=\frac{10.8}{2}=5.4$ inches.

Step2: Find the area of the two - circular bases

The area of a circle is $A_{base}=\pi r^{2}$. For two bases, $A_{bases}=2\pi r^{2}=2\pi(5.4)^{2}=2\pi\times29.16 = 58.32\pi$ square inches.

Step3: Calculate the lateral surface area

The lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$, where $h = 6$ inches. So $A_{lateral}=2\pi\times5.4\times6=64.8\pi$ square inches.

Step4: Calculate the total surface area

The total surface area $A = A_{bases}+A_{lateral}=58.32\pi+64.8\pi=123.12\pi$ square inches.
Using $\pi\approx3.14$, we have $A\approx123.12\times3.14 = 386.5968\approx387$ square inches.

For question 13:
A right - triangle rotated about one of its legs forms a cone. When a triangle is rotated about a given axis, the solid formed is a cone.

For the cross - section question:
A pyramid can have a triangular cross - section when sliced appropriately. A cone also can have a triangular cross - section when sliced through its vertex and perpendicular to the base.

Answer:

1. b) 387
2. d) Cone

For the cross - section question, both a pyramid and a cone can have a triangular cross - section. If we assume the most common cases, a cone sliced through its vertex and perpendicular to the base gives a triangular cross - section. But without more specific information about the slicing of the pyramid, if we have to choose one, for a simple and clear case of getting a triangular cross - section by a standard slicing method, we can consider a cone sliced through its vertex. However, this part of the question is a bit ambiguous without more details about the slicing of the pyramid. If we just focus on the general knowledge of shapes having triangular cross - sections, both are correct in a sense. If we must pick one answer option (assuming there is only one correct choice in a multiple - choice context), more information about the slicing of the pyramid is needed. But if we consider the typical way of getting a triangular cross - section for a single shape in a basic geometry context, we might say a cone (sliced through the vertex) is a more straightforward example. So, if we assume we are choosing between the given options for the cross - section question, we might say the shape that clearly shows a triangular cross - section when sliced in a standard way is a cone (sliced through the vertex). But again, this depends on the specific requirements of the problem.

If we are just answering the multiple - choice questions as presented and not getting too deep into the cross - section ambiguity:

1. b) 387
2. d) Cone

For cross - section: (assuming we consider a cone as the answer based on the simplicity of getting a triangular cross - section by slicing through the vertex) d) Cone (assuming there is an option for cone in the cross - section multiple - choice which is not fully shown in the provided text but based on the analysis above)