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

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.

step-by-step explanation: