Find the surface area of the right cylinder if the diameter is 28 in, and the height is 9 in. Round to the nearest 100th.

A. 1231.5 in²
B. 5541.77 m²
C. 2023.19 m²
D. 1407.43 m²



Answer :

To find the surface area of a right cylinder given the diameter of 28 inches and the height of 9 inches, follow these steps:

1. Calculate the radius of the cylinder:
The radius [tex]\( r \)[/tex] is half of the diameter [tex]\( d \)[/tex].
[tex]\[ r = \frac{d}{2} = \frac{28}{2} = 14 \text{ inches} \][/tex]

2. Calculate the lateral surface area of the cylinder:
The formula for the lateral surface area of a cylinder is [tex]\( 2\pi rh \)[/tex].
[tex]\[ \text{Lateral Area} = 2\pi rh = 2\pi (14)(9) \][/tex]
Plugging in the values:
[tex]\[ \text{Lateral Area} = 2 \times \pi \times 14 \times 9 = 791.68 \text{ square inches} \quad (\text{approx.}) \][/tex]

3. Calculate the area of one base:
The formula for the area of a circle is [tex]\( \pi r^2 \)[/tex].
[tex]\[ \text{Base Area} = \pi r^2 = \pi (14)^2 \][/tex]
Plugging in the values:
[tex]\[ \text{Base Area} = \pi \times 14^2 = 615.75 \text{ square inches} \quad (\text{approx.}) \][/tex]

4. Calculate the total surface area:
The total surface area of the cylinder includes the lateral surface area and the area of the two bases.
[tex]\[ \text{Total Surface Area} = \text{Lateral Area} + 2 \times \text{Base Area} \][/tex]
Plugging in the previously calculated values:
[tex]\[ \text{Total Surface Area} = 791.68 + 2 \times 615.75 = 791.68 + 1231.50 = 2023.18 \text{ square inches} \quad (\text{approx.}) \][/tex]

5. Round the total surface area to the nearest hundredth:
The final result is:
[tex]\[ 2023.19 \text{ square inches} \][/tex]

Therefore, the surface area of the right cylinder with a diameter of 28 inches and a height of 9 inches, rounded to the nearest hundredth, is [tex]\(\boxed{2023.19 \text{ square inches}}\)[/tex].