math 1012 question 3

Question

find the area enclosed by the figure. Use 3.14 for .

the inclose circle is 7yd's

Answer 1

The question has no "FIGURE" to refer to, and I'm not sure what you mean when you state "inclose circle is 7 yds". IF, AND ONLY IF, you mean the DIAMETER is 7 yards, here is the solution.

Area of a Circle = π R²

Pi = 3.14 Assumed in the problem.

R = Radius = One-half of the DIAMETER of 7 yards = 3.5

Area = (3.14) (3.5)²

Area = (3.14) (12.25)

Area = 38.465 sq yds

ANSWER: Area of a circle with a DIAMETER of 7 yards is 38.465 sq yds.

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If, on the other hand, you mean the distance AROUND THE CIRCLE, which is the CIRCUMFERENCE, is 7 yards, here is the solution.

Let C = the CIRCUMFERENCE of the circle, or 7 yards

Let D = the DIAMETER of the circle

In all circles, the distance around the circle is always a little more than three times across the circle. Or, the CIRCUMFERENCE is equal to the DIAMETER times PI.

Therefore, C = (PI)(D)

C = π D

7 = (3.14) D Assuming the circumference is 7 yards and pi is 3.14

7 (3.14) D

-------- = ---------- Dividing both sides of the equation by 3.14 to isolate D.

3.14 3.14

2.2292 = D

Since the DIAMETER is twice the size of the RADIUS, divide 2.2292 by 2.

Radius = 2.2292/2 = 1.1146 yards

Area of the circle = (Pi) R²

Area of the circle = (3.14) (1.1146)²

Area of the circle = (3.14) (1.2423)

Area of the circle = 3.9008 sq yds

ANSWER IF CIRCUMFERENCE IS 7 YARDS:

Area = 3.9008 sq yds

Hope this was helpful April.