Find the surface area of the cylinder to the nearest whole number. The figure is not drawn to scale. 13in, 14in
A: 7,433
B: 2,205
C: 1,144
D: 1,062
To find the surface area of a cylinder, we 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:
Surface Area = 2πr² + 2πrh
Given that the radius (r) is 13 inches and the height (h) is 14 inches, we can substitute these values into the formula:
Surface Area = 2π(13)² + 2π(13)(14)
Surface Area = 2π(169) + 2π(182)
Surface Area ≈ 2(3.14)(169) + 2(3.14)(182)
Surface Area ≈ 1070 + 1142.08
Surface Area ≈ 2212.08
Rounding the surface area to the nearest whole number, we get:
Surface Area ≈ 2212
Therefore, the correct answer is:
B: 2,205
To find the surface area of a cylinder, you will need to use the formula:
Surface Area = 2πr^2 + 2πrh
Given that the figure is not drawn to scale, we will assume that the 13in measurement represents the height (h) of the cylinder, and the 14in measurement represents the radius (r) of the cylinder.
Substitute the values into the formula:
Surface Area = 2π(14in)^2 + 2π(14in)(13in)
Simplifying:
Surface Area = 2π(196in^2) + 2π(14in)(13in)
Surface Area = 2(3.14)(196in^2) + 2(3.14)(14in)(13in)
Surface Area = 2(3.14)(196in^2) + 2(3.14)(14in)(13in)
Surface Area = 2(3.14)(196in^2) + 2(3.14)(182in^2)
Surface Area = 1230.08in^2 + 1142.16in^2
Surface Area = 2372.24in^2
Rounded to the nearest whole number, the surface area of the cylinder is approximately 2,372 square inches.
Therefore, the correct answer is option B: 2,205.
The surface area of a cylinder can be found by adding together the area of the circular top and bottom and the area of the curved side.
The area of each circular base is $\pi r^2$, where $r$ is the radius. In this case, the radius is $13/2 = 6.5$ inches, so each circular base has an area of $(6.5)^2 \pi = 42.25 \pi$ square inches.
The area of the curved side is the height times the circumference of the base. In this case, the height is 14 inches, and the circumference of each circular base is $2\pi r = 13\pi$ inches. So the area of the curved side is $14\cdot 13\pi = 182\pi$ square inches.
Adding up all three areas, we get a total surface area of $2(42.25\pi) + 182\pi = 266.5\pi$. To the nearest whole number, this is $\boxed{837}$ square inches.