Question

A circle is divided into 4 sector in the ratio 4,3,1 and 2 .the circumference of the circle is 190cm.calculate

i.the area of the circle
ii.the length of the arc of the smaller sector
III. the area of the smallest sector​

Answer 1

To solve the problem, calculate the circumference and radius of the circle using the given information. Then, find the central angles of the sectors and calculate the lengths of the arcs using the radius and central angles. Finally, calculate the area of the smallest sector using the radius and its central angle.

Step-by-step explanation:

To solve this problem, we can start by finding the circumference of the whole circle. Given that the circumference is 190cm, we can use the formula C = 2πr to find the radius of the circle. Using the formula C = 2πr, we can solve for r by dividing 190cm by 2π. Once we find the radius, we can use it to calculate the area of the entire circle using the formula A = πr². Now, to find the length of the arc of the smaller sector, we need to calculate the central angle of that sector. Let's assume the central angle of the whole circle is 360°. Since the largest sector has a ratio of 4 and the sum of the ratios is 4+3+1+2 = 10, we can find the central angle of the largest sector by multiplying 360° by the ratio 4/10. Similarly, we can find the central angles of the other sectors by multiplying 360° by their respective ratios. Once we have the central angles, we can find the lengths of the arcs of the sectors by using the formula L = 2πr(θ/360°). Finally, the area of the smallest sector can be found using the formula A = πr²(θ/360°).

Answer 2

i. area of the circle = 2872.75 cm²

ii. length of the arc of the smaller sector = 19 cm

III. area of the smallest sector = 287.3 cm²

Step-by-step explanation:

The formula for calculating the circumference of any circle is 2*π*r

The formula for calculating the area of any circle is π*r²

1. "forget" all extra info and concentrate on the one important piece of info, which is circumference of the circle is 190cm. Use the right formula and calculate r.

2*π*r = 190

r = (190)/(2*π)

r = 30.2394391874601

r = 30,24 cm

2. Now use r in the other formula to calculate the total area of the circle in cm².

π* 30.2394391874601)² = 2872.75 cm²

3. Given there are 4 sector in the ratio 4,3,1,2. the total number of ratios is the sum of 4+3+1+2 = 10.

Wich means that 10 ratios account for the total area of the circle. and also for the the total circumference.

The smaller sector has the ratio of 1, which accounts for 1/10 arc of the total circomference:

1/10 *190 = 19 cm

4. The smaller sector has the ratio of 1, which accounts for 1/10 part of the total area:

1/10 * 2872.75 = 287.3 cm²

And that's all there is to it.