To find the surface area of a slanted cylinder, we need to calculate both the lateral surface area and the area of the two circular bases. However, if the cylinder is slanted, it typically implies that we will still use the height directly relevant to the base radius for the lateral surface area calculation.
The formula for the surface area (SA) of a cylinder is given by:
\[ SA = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius,
- \( h \) is the height.
Given:
- Radius \( r = 5 \) cm
- Height \( h = 15 \) cm
Step 1: Calculate each part of the surface area
-
Area of the two bases: \[ 2\pi r^2 = 2\pi (5^2) = 2\pi (25) = 50\pi \]
-
Lateral Surface Area: \[ 2\pi rh = 2\pi (5)(15) = 150\pi \]
Step 2: Add both areas
\[ SA = 50\pi + 150\pi = 200\pi \]
Step 3: Calculate the numerical value
Using the value of \( \pi \approx 3.14 \): \[ SA \approx 200 \times 3.14 \approx 628 \]
Conclusion
The surface area of the slanted cylinder is approximately 628 square centimeters when rounded to the nearest whole number.
So, the correct answer is:
628 square centimeters