Question

12 of 1312 of 13 Items
the top of the cylinder is 5 inches the side is 4 inches and the bottom is 5 inches

Question
Calculate the surface area of the net diagram of the right circular cylinder. Use 3.14 for π
.

(1 point)
Responses

157 inches2
157 inches 2

282.6 inches2
282.6 inches 2

141.3 inches2
141.3 inches 2

197 inches2

the answer isnt 102 your wrong

Answer 1

To calculate the surface area of a right circular cylinder, we use the formula:

\[
\text{Surface Area} = 2\pi r(h + r)
\]

where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.

From your description, it seems that the top and bottom diameters are given as 5 inches, meaning the radius \( r \) is half of the diameter:

\[
r = \frac{5}{2} = 2.5 \text{ inches}
\]

The height of the cylinder is given as 4 inches.

Now substituting the values into the surface area formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 2.5 \times (4 + 2.5)
\]

Calculating the height plus radius:

\[
h + r = 4 + 2.5 = 6.5 \text{ inches}
\]

Now substitute this back into the surface area formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 2.5 \times 6.5
\]

Calculating step by step:

1. Calculate \( 2 \times 3.14 \):
\[
2 \times 3.14 = 6.28
\]

2. Calculate \( 6.28 \times 2.5 \):
\[
6.28 \times 2.5 = 15.7
\]

3. Finally, calculate \( 15.7 \times 6.5 \):
\[
15.7 \times 6.5 = 102.05
\]

4. This is the total surface area of the cylinder; however, we need to remember to multiply by 2 for the top and bottom areas:

The area of the top and bottom (circles) is:
\[
2 \times (\pi r^2) = 2 \times 3.14 \times (2.5)^2 = 2 \times 3.14 \times 6.25 = 39.25
\]

Adding the lateral area (side area):
\[
\text{Lateral Area} = 15.7 \times 6.5 = 102.05
\]

So, the entire Surface Area will be:
\[
\text{Total Surface Area} = 39.25 + 102.05 = 141.3 \text{ inches}^2
\]

The answer is **141.3 inches²**.