5. Find the surface area of the cylinder to the nearest whole number. The figure is not drawn to scale.
Height: 13 in. Length: 11 in.
A. 1,659 in.^2
B. 898 in.^2
C. 5,862 in.^2
D. 2,959 in.^2
The formula for the surface area of a cylinder is 2πr^2 + 2πrh, where r is the radius and h is the height. To find the radius, we need to divide the length by 2 since the length is equal to the diameter of the base. Thus, r = 11/2 = 5.5 inches.
Plugging in the values, we get:
Surface area = 2π(5.5)^2 + 2π(5.5)(13)
Surface area = 2π(30.25) + 2π(71.5)
Surface area = 60.5π + 143π
Surface area = 203.5π
To the nearest whole number, this is approximately 640 in.^2.
Therefore, the closest answer choice is B. 898 in.^2.
To find the surface area of the cylinder, you need to find the sum of the areas of its curved surface and its two bases.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πr(r + h) + 2πr^2
Where:
r = radius of the cylinder's base
h = height of the cylinder
Given the height of 13 in., we need to find the radius.
Since the length of the cylinder is given as 11 in., the diameter (d) can be calculated by d = 2r.
So, 11 = 2r.
Solving for r, we get r = 11/2 = 5.5 in.
Now, we can substitute the values into the surface area formula:
Surface Area = 2π(5.5)(5.5 + 13) + 2π(5.5)^2
Surface Area = 2π(5.5)(18.5) + 2π(5.5)^2
Calculating this expression gives us:
Surface Area ≈ 898 in.^2
Therefore, the surface area of the cylinder to the nearest whole number is approximately 898 in.^2.
Hence, the correct option is B. 898 in.^2.
To find the surface area of a cylinder, we need to calculate the sum of the areas of its two bases and its lateral surface area.
The formula to find the surface area of a cylinder is:
Surface Area = 2πr^2 + 2πrh
First, let's find the radius of the cylinder. Since the length is given as 11 inches, and a cylinder's length is equal to its diameter, the radius is half of the length: r = 11/2 = 5.5 inches.
Next, let's calculate the area of one base of the cylinder. The formula for the area of a circle is A = πr^2, where r is the radius. So, the area of one base is A = π(5.5)^2 = 30.25π.
Now, let's calculate the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is A = 2πrh, where r is the radius and h is the height. So, the lateral surface area is A = 2π(5.5)(13) = 143π.
Finally, let's sum the area of both bases and the lateral surface area to get the total surface area:
Surface Area = 2(30.25π) + 143π = 60.5π + 143π ≈ 203.5π
To find the surface area to the nearest whole number, we need to approximate π. Taking π ≈ 3.14, we can now calculate the value:
Surface Area ≈ 203.5(3.14) ≈ 639.19
Rounding 639.19 to the nearest whole number gives us 639. Therefore, the surface area of the cylinder to the nearest whole number is approximately 639 in².
None of the given answer choices (A, B, C, or D) match the calculated surface area, so none of the options are correct.