The radius of a cylinder is 3.5 ft. The height is 14 ft. Find the surface area and volume of the cylinder to the nearest tenth of a foot. Show your work.
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Show us your effort and we'll check it.
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What you really mean is that you need to LEARN a lot by Friday.
Here's a start.
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To find the surface area of a cylinder, you need to calculate the areas of the two circular bases, as well as the lateral surface area which is the area of the curved side.
1. Circular Base Area: The formula to find the area of a circle is A = π * r^2.
Given the radius, r = 3.5 ft, substitute it into the formula to find the area of one circular base.
A1 = π * (3.5)^2
2. Lateral Surface Area: The lateral surface area of a cylinder is given by the formula A = 2 * π * r * h.
Given the radius, r = 3.5 ft, and the height, h = 14 ft, substitute these values in the formula.
A2 = 2 * π * 3.5 * 14
3. Total Surface Area: To find the total surface area, add both the circular base areas and the lateral surface area.
A_total = 2 * A1 + A2
To find the volume of the cylinder, you need to calculate the volume of the cylindrical shape, using the formula:
Volume = A1 * h, where A1 is the area of one circular base, and h is the height.
4. Volume:
V = A1 * h
Now, let's calculate the values.
1. Circular Base Area:
A1 = 3.14 * (3.5)^2
2. Lateral Surface Area:
A2 = 2 * 3.14 * 3.5 * 14
3. Total Surface Area:
A_total = 2 * A1 + A2
4. Volume:
V = A1 * h
Once you substitute the values and perform the calculations, you will get the surface area and volume of the cylinder to the nearest tenth of a foot.