Question

You walk around a circular pond of radius 13 miles for angle of theta = 10 degrees degree Which one of the following shows the distance you walked around the pond? (Take pi approx 3.14)

(A) 0.27 miles
(B) 10 miles
(C) 2.27 miles
(D) 1.3 miles

Answer 1

(C) 2.27 miles

Explanation:

Without doing any detailed calculation, you can estimate the distance. The angle of 10° is 1/36 of the full circle of 360°. The circumference is given by the formula ...

C = 2πr = 2(3.14)(13)

We want to find 1/36 of that circumference, which will be about ...

C/36 = (3.14)(2)(13)/36 ≈ 3.14(2/3) ≈ 2

This is sufficiently accurate to determine that the best choice is (C).

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If you want to use a calculator, you can figure the distance as ...

C/36 = (3.14)(26/36) ≈ 2.26777...(repeating) ≈ 2.27 . . . miles