Question

4 which figure is a net for a cube? a figure a b figure b c figure c d figure d 5 pedro uses cardboard to make a model of a square pyramid. the edges of the base of the model are 5 in. long. the height of each triangular face is 4 in. what is the area of the cardboard in pedro’s model? show your work.

Explanation:

Step1: Recall cube - net properties

A cube has 6 square faces. A valid net for a cube can be folded to form a cube without overlapping.

Step2: Analyze option A

Option A has 7 squares, while a cube has 6 faces, so it is not a net for a cube.

Step3: Analyze option B

Option B has 8 squares, so it is not a net for a cube.

Step4: Analyze option C

Option C has a pattern that cannot be folded to form a cube without overlapping.

Step5: Analyze option D

Option D is a valid net for a cube. It can be folded to form a cube with 6 square faces.

for question 5:

Step1: Calculate the area of the base

The base of the square - pyramid is a square. The area of a square is given by \(A_{base}=s^{2}\), where \(s = 5\) in. So \(A_{base}=5^{2}=25\) square inches.

Step2: Calculate the area of one triangular face

The area of a triangle is given by \(A_{triangle}=\frac{1}{2}bh\), where \(b = 5\) in (base of the triangle, which is the side - length of the square base) and \(h = 4\) in (height of the triangular face). So \(A_{triangle}=\frac{1}{2}\times5\times4 = 10\) square inches.

Step3: Calculate the total area of the four triangular faces

Since there are 4 triangular faces, \(A_{triangles}=4\times A_{triangle}=4\times10 = 40\) square inches.

Step4: Calculate the total surface area of the square - pyramid

The total surface area \(A = A_{base}+A_{triangles}\). So \(A=25 + 40=65\) square inches.

Answer:

D