Use the image to answer the question.
An illustration shows a horizontal rectangle of height 4 inches with a circle of radius 8 inches attached to its top left and a circle of radius 8 inches attached to its bottom right.
Find the surface area of the net diagram of the right circular cylinder. Use 3.14 for π .
(1 point)
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To find the surface area of the net diagram of the right circular cylinder, we need to calculate the areas of the two circles (top and bottom) and the lateral surface area of the rectangle.
1. Area of the top and bottom circles:
Each circle has a radius of 8 inches, so the area of one circle is:
A = πr^2
A = 3.14 * 8^2
A = 3.14 * 64
A = 200.96 square inches
Since there are two circles, the total area of both circles is:
Total area = 2 * 200.96
Total area = 401.92 square inches
2. Lateral surface area of the rectangle:
The rectangle has a width (which is also the diameter of the circles) of 16 inches and a height of 4 inches. The lateral surface area of the rectangle is:
A = perimeter * height
A = (2 * width + 2 * height) * height
A = (2 * 16 + 2 * 4) * 4
A = (32 + 8) * 4
A = 40 * 4
A = 160 square inches
3. Total surface area of the net diagram:
Total surface area = total area of circles + lateral surface area of rectangle
Total surface area = 401.92 + 160
Total surface area = 561.92 square inches
Therefore, the surface area of the net diagram of the right circular cylinder is 561.92 square inches.