What is the surface area of the cylinder in terms of pi? the diagram is not drawn to scale.
Radius=8 inches
Height=20 inches
a) 352 pi in^2
b) 320 pi in^2
c) 832 pi in ^2
d) 448 pi in^2
The formula for the surface area of a cylinder is 2πr² + 2πrh, where r is the radius and h is the height.
Plugging in the values given, we get:
Surface Area = 2π(8²) + 2π(8)(20)
Surface Area = 128π + 320π
Surface Area = 448π
Therefore, the surface area of the cylinder in terms of pi is 448π in², which corresponds to (d) in the answer choices.
To find the surface area of a cylinder, you need to calculate the sum of the areas of the two bases and the lateral surface area. The formula for the surface area of a cylinder is 2πr² + 2πrh, where r is the radius and h is the height.
Given:
Radius (r) = 8 inches
Height (h) = 20 inches
First, calculate the area of the bases:
Base Area = πr²
Substituting the value of r:
Base Area = π(8)² = 64π in²
Next, calculate the lateral surface area:
Lateral Surface Area = 2πrh
Substituting the values of r and h:
Lateral Surface Area = 2π(8)(20) = 320π in²
Finally, add the area of the two bases and the lateral surface area together:
Surface Area = 2πr² + 2πrh = 64π in² + 320π in² = 384π in²
Therefore, the correct answer is none of the options provided. The surface area of the cylinder in terms of π is 384π in².
To find the surface area of a cylinder, we need to consider two parts: the two circular bases and the curved surface.
The formula for the surface area of a cylinder is:
Surface Area = 2πr² + 2πrh
Where:
- π is a mathematical constant, approximately equal to 3.14159.
- r is the radius of the cylinder.
- h is the height of the cylinder.
From the given information:
- Radius = 8 inches
- Height = 20 inches
Let's calculate the surface area:
1. Area of the circular bases:
The formula for the area of a circle is:
Area = πr²
For the top and bottom bases, substitute the radius (r = 8 inches) into the formula:
Area of each base = π * (8 inches)²
2. Curved Surface area:
The formula for the lateral surface area of a cylinder is:
Lateral surface area = 2πrh
Substitute the radius (r = 8 inches) and height (h = 20 inches) into the formula:
Lateral surface area = 2π * (8 inches) * (20 inches)
Now, calculate the individual areas:
1. Area of the circular bases:
Area = π * (8 inches)² = 64π square inches
(We have two bases, so the total area of both bases is 2 * 64π = 128π square inches)
2. Curved Surface area:
Lateral surface area = 2π * 8 inches * 20 inches = 320π square inches
Finally, find the total surface area by adding both the areas we calculated:
Total Surface Area = (Area of bases) + (Curved Surface area)
Total Surface Area = 128π + 320π = 448π square inches
Therefore, the surface area of the cylinder in terms of π is 448π square inches.
So, the correct answer is (d) 448π in².