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
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
To find the approximate surface area of the cylinder, we need to use the formula:
Surface Area = 2πr² + 2πrh
First, let's identify the values we have. We have the height of the cylinder, which is 9m. However, we don't have the radius of the cylinder directly given. But we can calculate it by using the information given in the net of the cylinder:
5m
9m
5m
5m
9m
Since the net is not drawn to scale, we need to make an assumption about the dimensions. Let's assume that the 5m edges are the base edges of the cylinder. From the net, we can see that there are two circles, one at the top and one at the bottom of the cylinder.
To calculate the radius, we can divide the circumference of the circle by 2π. The circumference of the circle can be calculated using the given width of 5m:
Circumference = πd
Since the width is 5m, the diameter (d) would be the same. So,
Circumference = π × 5m
Now, let's calculate the radius:
Radius = Circumference / 2π
Plugging in the value, we get:
Radius = (π × 5m) / 2π
Using cancelation, we get:
Radius = 5m / 2
Which simplifies to:
Radius = 2.5m
Now that we have the radius and height, we can substitute these values into the surface area formula:
Surface Area = 2π(2.5m)² + 2π(2.5m)(9m)
Simplifying further:
Surface Area = 2π(6.25m²) + 2π(22.5m²)
Surface Area = 12.5πm² + 45πm²
Surface Area = 57.5πm² (approximate value)
To find the answer to the nearest square meter, we need to use the value of π (pi). Approximating π to 3.14:
Surface Area ≈ 57.5 × 3.14 m²
Surface Area ≈ 180.85 m²
Therefore, the approximate surface area of the cylinder, rounded to the nearest square meter, is 181 m².
To find the surface area of the cylinder, we can use the formula:
Surface Area = 2πr(r + h)
Where r is the radius of the circular base and h is the height of the cylinder.
Given the dimensions:
Radius (r) = 5m
Height (h) = 9m
Substituting these values into the formula:
Surface Area = 2π(5)(5 + 9)
Calculating the expression within the parentheses:
Surface Area = 2π(5)(14)
Multiplying:
Surface Area = 2π(70)
Calculating the product of 2π:
Surface Area ≈ 440m²
Therefore, the approximate surface area of the cylinder is 440 square meters. Hence the answer is:
O 440 m²