IDNLearn.com: Your one-stop destination for reliable answers to diverse questions. Our platform provides trustworthy answers to help you make informed decisions quickly and easily.

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


Sagot :

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].