Unit 7 lesson 12 cones cylinders and spheres unit test help pls
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Find the lateral surface area of a cylinder with a radius of 2.5 meters and a height of 7 meters. Use 3.14 for pi and round your answer to the nearest tenth.
The lateral surface area of a cylinder can be found using the formula:
Lateral Surface Area = 2πrh
Given:
Radius (r) = 2.5 meters
Height (h) = 7 meters
Pi (π) = 3.14
Substituting these values into the formula:
Lateral Surface Area = 2 * 3.14 * 2.5 * 7
Calculating this:
Lateral Surface Area = 3.14 * 5 * 7
Lateral Surface Area = 109.9 square meters (rounded to the nearest tenth)
Therefore, the lateral surface area of the cylinder is approximately 109.9 square meters.
What is the total surface area of the cylinder from part a
The total surface area of a cylinder can be found by adding the areas of the two bases (which are circles) and the lateral surface area.
Given:
Radius (r) = 2.5 meters
Height (h) = 7 meters
Pi (π) = 3.14
To find the area of a circle, we use the formula:
Area = πr^2
Area of the base (circle):
Area of the base = 3.14 * (2.5)^2
Area of the base = 3.14 * 6.25
Area of the base = 19.625 square meters
The total surface area is then given by:
Total Surface Area = 2 * (Area of the base) + (Lateral Surface Area)
Lateral Surface Area (calculated in question a) = 109.9 square meters
Therefore,
Total Surface Area = 2 * 19.625 + 109.9
Total Surface Area = 39.25 + 109.9
Total Surface Area = 149.15 square meters (rounded to the nearest tenth)
Hence, the total surface area of the given cylinder is approximately 149.15 square meters.