To find the area of a circle, we use the formula:
[tex]\[ \text{Area} = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle and [tex]\( \pi \)[/tex] is approximately [tex]\(\frac{22}{7}\)[/tex].
Let's solve for each given radius step-by-step:
### (a) Radius: 7 cm
The formula for the area is:
[tex]\[ \text{Area} = \pi r^2 \][/tex]
Substituting [tex]\(\pi = \frac{22}{7}\)[/tex] and [tex]\(r = 7\)[/tex],
[tex]\[ \text{Area} = \frac{22}{7} \times 7^2 \][/tex]
[tex]\[ \text{Area} = \frac{22}{7} \times 49 \][/tex]
[tex]\[ \text{Area} = 22 \times 7 \][/tex]
[tex]\[ \text{Area} = 154 \, \text{cm}^2 \][/tex]
### (b) Radius: 14 cm
Using the same formula:
[tex]\[ \text{Area} = \frac{22}{7} \times 14^2 \][/tex]
[tex]\[ \text{Area} = \frac{22}{7} \times 196 \][/tex]
[tex]\[ \text{Area} = 22 \times 28 \][/tex]
[tex]\[ \text{Area} = 616 \, \text{cm}^2 \][/tex]
### (c) Radius: 2.1 cm
Using the formula:
[tex]\[ \text{Area} = \frac{22}{7} \times 2.1^2 \][/tex]
[tex]\[ 2.1 = \frac{21}{10} \][/tex]
First, calculate [tex]\(2.1^2\)[/tex]:
[tex]\[ 2.1^2 = 4.41 \][/tex]
Substituting back,
[tex]\[ \text{Area} = \frac{22}{7} \times 4.41 \][/tex]
[tex]\[ \text{Area} \approx 13.86 \, \text{cm}^2 \][/tex]
### (d) Radius: 8.4 cm
Using the formula:
[tex]\[ \text{Area} = \frac{22}{7} \times 8.4^2 \][/tex]
[tex]\[ 8.4 = \frac{84}{10} \][/tex]
Calculate [tex]\(8.4^2\)[/tex]:
[tex]\[ 8.4^2 = 70.56 \][/tex]
Substituting back,
[tex]\[ \text{Area} = \frac{22}{7} \times 70.56 \][/tex]
[tex]\[ \text{Area} \approx 221.76 \, \text{cm}^2 \][/tex]
Therefore, the areas of the circles with the given radii are:
(a) [tex]\(154 \, \text{cm}^2\)[/tex]
(b) [tex]\(616 \, \text{cm}^2\)[/tex]
(c) [tex]\(13.86 \, \text{cm}^2\)[/tex]
(d) [tex]\(221.76 \, \text{cm}^2\)[/tex]
