a circle, with a diameter 48 cm is cut into 12 equal sectors. a square, with a side length 41cm, is cut into 16 equal squares. wich has the greatesst area? how much greater is it
circle: radius = 24
area = π(24^2 = 576π
cut into 12 equal sectors, so each sector = 48π cm^2 or appr. 150.8 cm^2
square: side = 41
area = 41^2 = 1681 cm^2
cut into 16 equal squares, so each square = appr. 105.06 cm^2
is correct
To find out which shape has the greatest area, we need to calculate the areas of both shapes and compare them.
Let's start with the circle. The radius of the circle can be found by halving the diameter, so the radius r = 48 cm / 2 = 24 cm. The area of a circle is given by the formula A = πr^2, where π is a constant equal to approximately 3.14. Substituting the radius into the formula, we get A = 3.14 * (24 cm)^2 = 3.14 * 576 cm^2 ≈ 1,810.56 cm^2.
Now let's move on to the square. The area of a square is given by the formula A = side length^2. For the given square, the side length is 41 cm. So the area of the square is A = (41 cm)^2 = 1,681 cm^2.
Comparing the two areas, we can see that the circle has a greater area than the square by approximately 1,810.56 cm^2 - 1,681 cm^2 = 129.56 cm^2. Therefore, the circle has a greater area than the square, and it is approximately 129.56 cm^2 greater.
To determine which shape has the greatest area and by how much it is greater, we need to calculate the areas of both shapes.
Let's start with the circle:
- The diameter of the circle is 48 cm, which means the radius is half of that, i.e., 48/2 = 24 cm.
- To find the area of a circle, we use the formula A = πr^2, where A is the area and r is the radius.
- Plugging in the values we have, the area of the circle is A = π(24)^2 = 576π cm^2.
Now let's calculate the area of the square:
- The side length of the square is given as 41 cm.
- The area of a square can be found by multiplying the length of any side by itself, so A = s^2, where A is the area and s is the side length.
- Substituting the given side length, the area of the square is A = (41)^2 = 1681 cm^2.
Comparing the two areas, we have:
- Circle area = 576π cm^2
- Square area = 1681 cm^2
To determine which shape has the larger area, we need to calculate the numerical value of π (pi). π is approximately equal to 3.14.
- Circle area ≈ 576 × 3.14 = 1806.24 cm^2
Comparing the two areas, we find that the square has a greater area. The difference between the areas is:
- Difference = Square area - Circle area = 1681 - 1806.24 = -125.24 cm^2 (rounded to two decimal places)
Therefore, the square has a greater area than the circle, but the difference between their areas is approximately -125.24 cm^2. The negative value indicates that the circle's area is larger.