To find the surface area of the cylinder, we need to find the areas of the two circles (bases) and the rectangle (lateral surface) and add them together.
The area of a circle is given by the formula A = π * r^2, where A is the area, and r is the radius.
The area of a rectangle is given by the formula A = length * width, where A is the area.
Since we have two circles with a radius of 5m,
Area of the bases (Both circles) = 2 * π * 5^2 = 2 * π * 25 ≈ 2 * 78.54 = 157.08 m².
Now, we need to find the area of the rectangle. From the given dimensions, the rectangle has a length of 9m and a width equal to the circumference of the circle, which is given by C = 2 * π * r.
Rectangle width (circumference) = 2 * π * 5 ≈ 2 * 15.7 = 31.4 m.
Now, we can find the area of the rectangle:
Area of the rectangle (lateral surface) = length * width = 9 * 31.4 ≈ 283 m²
Finally, we need to add the areas of the bases and the rectangle to find the total surface area of the cylinder:
Total Surface Area ≈ 157.08 m² (bases) + 283 m² (rectangle) ≈ 440 m²
The approximate surface area of the cylinder is 440 m². So the answer is:
O 440 m²
9. Use the net to find the approximate surface area of the cylinder to the nearest square meter.
5 m
9m
5m
5m
9m
Not drawn to scale
O 440 m²
O 314 m²
O 283 m2²
O 214 m²
1 answer