Question

Meghan unfolded a three dimensional solid and formed the two dimensional figure below. Select all the statements that apply to this figure

Answer 1

Answer:

The statements that apply to this figure are:

• 3. The surface area is the lateral area plus the area of the two circles.

• 4. This is the net of a cylinder.

• 5. The lateral area is the circumference of the circle multiplied by the height of the solid.

Explanation:

First, analyze the 2D figure and imagine what it is in 3D: you may bend the left circle 90º, then roll it along the line of the rectangle all the way up and then bend the other circle 90º.

The rectangle will become the lateral walls of a cylinder and each circle a base.

Thus, the net corresponds to a cylinder.

Now, check every statementÑ

1. This is the net of a cone

• FALSE. It is a cylinder

2. The volume is found by adding up the areas of the circles and the rectangle.

FALSE. By adding up the areas of the circles and the rectangle you get the area of the cylinder.

3. The surface area is the lateral area plus the area of the two circles.

TRUE. The lateral area of the cylinder is equal to the area of the rectangle. The area of the two circles is the area of the bases of the cylinder.

By adding the lateral area and the area of the bases you get the total surface area of the cylinder.

4. This is the net of a cylinder.

TRUE. Explained above

5. The lateral area is the circumference of the circle multiplied by the height of the solid.

TRUE. The circumference of the circle is equal to the length of the rectangle. Thus, by multiplying this by the height of the rectangle, which is the same height of the solid, you get the area of the rectangle and that is the lateral area of the cylinder.

6. The solid has 3 faces, 6 edges and 4 vertices.

FALSE. The only edges of the cylinder are the rims of the bases and a cylinder does not have vertices.

Answer 2

Hence, the true statements that apply in the figure are:

• The surface area is the lateral area plus the area of the two circles.
• This is a net of a cylinder.
• The lateral area is the circumference of the circle multiplied by the height of the solid.

Cylinder:

A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis. The perpendicular distance between the bases is the height, $'h'$ and the distance from the axis to the outer surface is the radius $'r'$ of the cylinder.

Here this unfold is of a cylinder as it has $2$ circulars bare and $1$ rectangle side of the surface.

Total surface area is equal to= Surface area of lateral area + 2 circular area.

Lateral area= height$\times$circumference of the circle.

This solid has 3 faces, 2 edges then, option 3,4,5 is true.

Volume of area$=\frac{1}{3} \pi r^{2}h$         [$r=4 cm\\h=13 cm$]

                          $=\frac{1}{3}\pi (4) ^{2} h\\=217.817 \ cm^{2} \\\simeq 218 \ cm^{2}$

Volume of cylinder$=\pi r^{2} h$

                               $=251.32 \ cm^{2} \\\simeq 251 \ cm^{2}$

Learn more about the topic of Cylinders: https://brainly.com/question/8124297