Answer the questions below to find the total surface area of the cylinder.

A cylinder with radius 0.5 inches and height 3 inches. A circle with radius 0.5 inches on each side of a rectangle with width 3 inches.
Find the area of the circles at the top and bottom of the cylinder.
1. The area of each circle is exactly ____ π square inches.
2. There are ____ identical circles in the cylinder.
3. So the total area of all the circles is ____ π square inches.

11 answers

1. The area of each circle is exactly 0.25 π square inches.
2. There are 2 identical circles in the cylinder.
3. So the total area of all the circles is 0.5 π square inches.
Find the area of the rectangle.
1. One side of the rectangle is ___ π in.
2. The other side of the rectangle is ____ inches.
3. The area of the rectangle is exactly ___ π square inches.
1. One side of the rectangle is 0.5 π in.
2. The other side of the rectangle is 3 inches.
3. The area of the rectangle is exactly 1.5 π square inches.
Find the total surface area of the cylinder.
The total surface area is exactly ___ π square inches.
The total surface area of the cylinder is calculated by adding the areas of the two circles at the top and bottom of the cylinder, and the area of the rectangle that wraps around the side of the cylinder.

Total surface area = 2* (area of circle) + (area of rectangle)
Total surface area = 2*(0.5π) + (1.5π)
Total surface area = π + 1.5π
Total surface area = 2.5π

Therefore, the total surface area of the cylinder is 2.5π square inches.
Find the area of the rectangle.
1. One side of the rectangle is 0.5 π in.
2. The other side of the rectangle is 3 inches.
3. The area of the rectangle is exactly 1.5 π square inches.
Is incorrect. Please provide the correct answer.
Apologies for the mistake. Let's find the correct area of the rectangle:

1. One side of the rectangle is 0.5π in.
2. The other side of the rectangle is 3 inches.
3. The area of the rectangle is calculated by multiplying the two sides:
Area = 0.5π * 3
Area = 1.5π square inches

Therefore, the correct area of the rectangle is 1.5π square inches.
That answer is identical to your previous answer.
Please provide a different and correct answer.
I apologize for the confusion. Let's correct the answer by calculating the area of the rectangle using the correct dimensions:

Given:
One side of the rectangle is 0.5π in.
The other side of the rectangle is 3 inches.

To find the area of the rectangle, we will multiply the two sides:

Area = (0.5π) * 3
Area = 1.5π square inches

Therefore, the correct area of the rectangle is 1.5π square inches. Thank you for your patience.
Therefore, the total surface area of the cylinder is 2.5π square inches.
This was also incorrect.
I apologize for the error. Let's recalculate the total surface area of the cylinder using the correct values.

Given:
- The area of each circle is 0.25π square inches.
- There are 2 identical circles in the cylinder, so the total area of both circles is 0.25π * 2 = 0.5π square inches.
- The area of the rectangle is 1.5π square inches.

To find the total surface area of the cylinder, we add the areas of the circles and the rectangle:

Total surface area = 0.5π + 1.5π
Total surface area = 2π square inches

Therefore, the correct total surface area of the cylinder is 2π square inches. Thank you for your patience.