The sector area of a region of a circle is 23 mi². The central angle, 0 (theta), is 25°. What is the radius?

1 answer:

4 0

The radius of the sector is 10.27 miles

<h3>How to find the radius of a sector?</h3>

The area of a sector can be represented as follows;

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅= 25 degrees

area of the sector = 23 miles²

area of a sector = ∅ / 360 × πr²

23 = 25 / 360 × πr²

cross multiply

23 × 360 = 25πr²

8280 = 25πr²

divide both sides by 25

πr² = 8280 / 25

πr² = 331.2

r² = 331.2 / 3.14

r² = 105.477707006

r = √105.477707006

r = 10.2702336877 miles

Therefore, the radius of the sector is 10.27 miles

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Using proportions, it is found that the life span of the person would be 14 years, 212 days and 22 hours shorter.

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2 packs a day for 35 years is 40 cigarettes a day for 12775 days, as $35 \times 365 = 12775$ .
Thus, a total of 511000 cigarettes, as $40 \times 12775 = 511000$ .
Assuming each cigarette costs 15 minutes of life, the person loses 7665000 minutes of life, as $15 \times 511000 = 7665000$

One year has 525600 minutes, thus the person loses 14 years of life, as $\frac{7665000}{525600} = 14.5833333$

Looking at the decimal part, the person loses 212 days of life, as $0.5833333 \times 365 = 212.916666655$
Again looking at the decimal part, 22 hours, as $0.916666655 \times 24 = 22$