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:
-
Calculate \( 2 \times 3.14 \): \[ 2 \times 3.14 = 6.28 \]
-
Calculate \( 6.28 \times 2.5 \): \[ 6.28 \times 2.5 = 15.7 \]
-
Finally, calculate \( 15.7 \times 6.5 \): \[ 15.7 \times 6.5 = 102.05 \]
-
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.