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

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