This taxi sign is 2.1 metres wide and 39cm tall. Assuming the ends are perfect semi-circles find the area in square metres to three significant figures -
area = 2.1(.39) m^2 = .819 m^2
Well, I'd say that's one big taxi sign! And it's a little curvy too, with those perfect semi-circle ends. Let's calculate the area step by step, using some math and a pinch of humor!
First, we need to find the radius of those semi-circles. Since the width of the sign is 2.1 meters, and each semi-circle makes up half of that width, we can divide it by 2 to find the radius. So, the radius is 2.1 meters divided by 2, which is 1.05 meters.
Now that we have the radius, we can calculate the area of each semi-circle. The formula for the area of a circle is πr^2, where π is the mathematical constant approximately equal to 3.14159. So, the area of each semi-circle is 3.14159 times the radius squared, which is (3.14159)(1.05)^2.
But hold on a second, there are two semi-circles! So, we need to double that area. Multiply by 2, and we get 2 times (3.14159)(1.05)^2.
Finally, let's calculate the area of the rectangular part of the sign. The height is given as 39 centimeters, which we should convert to meters by dividing by 100. So, the height is 0.39 meters.
To find the area of the rectangular part, we multiply the width (2.1 meters) by the height (0.39 meters). And there you have it!
Now, let's add up the area of the two semi-circles and the rectangular part to find the total area of the taxi sign.
To find the area of the taxi sign, we need to consider that the shape of the sign is a rectangle with two semi-circles on each end.
1. Calculate the area of the rectangle:
Area_rect = width × height
Given that the width of the sign is 2.1 meters and the height is 39 cm, we need to convert the height to meters before calculating the area.
1 meter = 100 cm
39 cm = 39/100 = 0.39 meters
Area_rect = 2.1 m × 0.39 m
2. Calculate the area of two semi-circles:
The diameter of the semi-circles is equal to the height of the sign, which is 39 cm (0.39 meters). We want to find the area of two semi-circles, so we need to find the area of one semi-circle first and then multiply it by 2.
The formula for the area of a semi-circle is given by:
Area_semi = (π × r^2) / 2
where r is the radius of the semi-circle.
Since the height of the sign is the diameter of each semi-circle, the radius is half of the height, which is 0.39/2 = 0.195 meters.
Area_semi = (π × 0.195^2) / 2
3. Total area of the taxi sign:
To find the total area, we add the area of the rectangle and the area of two semi-circles.
Total_area = Area_rect + (2 × Area_semi)
Now, let's calculate the area to three significant figures:
Area_rect = 2.1 m × 0.39 m = 0.819 m^2
Area_semi = (π × 0.195^2) / 2 ≈ 0.0596 m^2 (Using π = 3.14159)
Total_area = 0.819 m^2 + (2 × 0.0596 m^2) ≈ 0.938 m^2
Therefore, the area of the taxi sign, to three significant figures, is approximately 0.938 square meters.
To find the area of the taxi sign, you can divide it into two parts: the rectangular portion in the middle and the two semi-circles at the ends.
First, let's find the area of the rectangular portion. The width of the sign is given as 2.1 meters and the height as 39 cm. We need to convert the height to meters by dividing it by 100:
39 cm = 0.39 m
Now we can calculate the area of the rectangular portion:
Area of the rectangle = width × height = 2.1 m × 0.39 m = 0.819 m²
Next, let's find the area of the two semi-circles at the ends. The radius of each semi-circle is half of the height of the sign. Therefore, the radius is:
Radius = 0.39 m ÷ 2 = 0.195 m
To find the area of a semi-circle, we use the formula:
Area of a semi-circle = (π × radius²) ÷ 2
Plugging in the values, we can calculate the area of both semi-circles:
Area of both semi-circles = (π × 0.195 m²) ÷ 2
Now, let's calculate the total area by summing up the area of the rectangle and the area of the two semi-circles:
Total area = Area of the rectangle + Area of both semi-circles
Finally, you can use a calculator to find the solution, keeping the answer to three significant figures.