Question

use the formula $a = \pi r^2$ to find the area of each circle below. round off decimal answers to a single decimal place.

1. $a = \underline{\quad\quad}$ (use $\frac{22}{7}$.)

circle with radius 14 in.

1. $a = \underline{\quad\quad}$ (use 3.14.)

circle with radius 6.1 ft.

1. $a = \underline{\quad\quad}$ (use $\frac{22}{7}$.)

circle with radius 21 km.

in problems 4, 5, and 6, find the radius ($r = \frac{d}{2}$) as your first step in solving for the area.

1. $a = \underline{\quad\quad}$ (use $\frac{22}{7}$.)

circle with diameter $d = 14$ m.

1. $a = \underline{\quad\quad}$ (use $\frac{22}{7}$.)

circle with diameter $d = 10$ in.

1. $a = \underline{\quad\quad}$ (use 3.14.)

circle with diameter $d = 3.2$ yds.

Explanation:

Problem 1

Step1: Identify radius and formula

Radius \( r = 14 \) in, formula \( A=\frac{22}{7}r^2 \).

Step2: Substitute and calculate

\( A = \frac{22}{7} \times 14^2 = \frac{22}{7} \times 196 = 22 \times 28 = 616 \) square inches.

Step1: Identify radius and formula

Radius \( r = 6.1 \) ft, formula \( A = 3.14r^2 \).

Step2: Substitute and calculate

\( A = 3.14 \times 6.1^2 = 3.14 \times 37.21 \approx 116.8 \) square feet (rounded to one decimal).

Step1: Identify radius and formula

Radius \( r = 21 \) km, formula \( A=\frac{22}{7}r^2 \).

Step2: Substitute and calculate

\( A = \frac{22}{7} \times 21^2 = \frac{22}{7} \times 441 = 22 \times 63 = 1386 \) square kilometers.

Answer:

\( 616 \) square inches

Problem 2