Question

What is the surface area, in square millimeters, of the cylinder that is represented by the net? Express your

answer in terms of . The formula for area of a circle is A = r2 and for area of a rectangle is A = bh.

*LOOK AT PHOTO*

Answer 1

The net of a cylinder consists of two circles and one rectangle. The circles represent the top and bottom of the cylinder, and the rectangle represents the lateral surface area of the cylinder.

The diameter of each circle is 6.5 mm, which means the radius is half of that, or 3.25 mm. Using the formula for the area of a circle, the area of one circle is:

A = πr^2 = π(3.25)^2 ≈ 33.183 mm^2

Since there are two circles, the total area of the circles is:

2A = 2πr^2 ≈ 66.367 mm^2

The height of the cylinder, which is also the length of the rectangle, is given as 32 mm. The width of the rectangle is the same as the circumference of the circle, which is 2πr. Using the formula for the area of a rectangle, the area of the lateral surface of the cylinder is:

A = bh = (2πr)(h) = (2π)(3.25)(32) ≈ 208.202 mm^2

Finally, the total surface area of the cylinder is the sum of the areas of the circles and the lateral surface area:

Total surface area = 2A + A = 3A ≈ 274.771 mm^2

Therefore, the surface area of the cylinder is approximately 274.771 square millimeters.

Answer 2

The total area of the net is 719.82 square mm

Calculating the area of the net

From the question, we have the following parameters that can be used in our computation:

The net

The total area of the net is the sum of the individual shapes

Where, we have the following shapes and dimensions:

• Rectangle
• Two circles

Using the area formulas, we have the following:

Rectangle 1: 32 * π * 6.5 = 653.45

2 circles = 2 * π * (6.5/2)² = 66.37

Add up the individual areas

Area = 653.45 + 66.37

Evaluate the expression

Surface area = 719.82

Hence. the total area of the figure is 719.82 square mm