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Calculate the areas of circles with the following diameters π as 22/7. a) 14 cm, b) 7 cm, c) 42 cm, d) 21 cm

Mathematics

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4 parts
a

1.54 cm2\text{1.54 cm}^2

b

38.5 cm2\text{38.5 cm}^2

c

1386 cm2\text{1386 cm}^2

d

346.5 cm2\text{346.5 cm}^2

Step-by-step solution

8 steps

The area of a circle is given by the formula A=πr2A = \pi r^2, where rr is the radius. The radius is half of the diameter, r=d2r = \frac{d}{2}. We will use π=227\pi = \frac{22}{7}.

Part a· 2 steps

Diameter d=1.4 cmd = 1.4 \text{ cm}

  1. Calculate the radius and substitute into the area formula.

    r=1.4 cm2=0.7 cmr = \frac{1.4 \text{ cm}}{2} = 0.7 \text{ cm} A=227×(0.7 cm)2=227×0.49 cm2A = \frac{22}{7} \times (0.7 \text{ cm})^2 = \frac{22}{7} \times 0.49 \text{ cm}^2
  2. Simplify and calculate the area.

    A=22×0.497 cm2=22×0.07 cm2A = 22 \times \frac{0.49}{7} \text{ cm}^2 = 22 \times 0.07 \text{ cm}^2 A=1.54 cm2A = 1.54 \text{ cm}^2

    The area of the circle is 1.54 cm2\boxed{\text{1.54 cm}^2}.

Part b

38.5 cm2\text{38.5 cm}^2

Diameter d=7 cmd = 7 \text{ cm}

  1. Calculate the radius and substitute into the area formula.

    r=7 cm2=3.5 cmr = \frac{7 \text{ cm}}{2} = 3.5 \text{ cm} A=227×(3.5 cm)2=227×12.25 cm2A = \frac{22}{7} \times (3.5 \text{ cm})^2 = \frac{22}{7} \times 12.25 \text{ cm}^2
  2. Simplify and calculate the area.

    A=22×12.257 cm2=22×1.75 cm2A = 22 \times \frac{12.25}{7} \text{ cm}^2 = 22 \times 1.75 \text{ cm}^2 A=38.5 cm2A = 38.5 \text{ cm}^2

    The area of the circle is 38.5 cm2\boxed{\text{38.5 cm}^2}.

Part c

1386 cm2\text{1386 cm}^2

Diameter d=42 cmd = 42 \text{ cm}

  1. Calculate the radius and substitute into the area formula.

    r=42 cm2=21 cmr = \frac{42 \text{ cm}}{2} = 21 \text{ cm} A=227×(21 cm)2=227×441 cm2A = \frac{22}{7} \times (21 \text{ cm})^2 = \frac{22}{7} \times 441 \text{ cm}^2
  2. Simplify and calculate the area.

    A=22×4417 cm2=22×63 cm2A = 22 \times \frac{441}{7} \text{ cm}^2 = 22 \times 63 \text{ cm}^2 A=1386 cm2A = 1386 \text{ cm}^2

    The area of the circle is 1386 cm2\boxed{\text{1386 cm}^2}.

Part d

346.5 cm2\text{346.5 cm}^2

Diameter d=21 cmd = 21 \text{ cm}

  1. Calculate the radius and substitute into the area formula.

    r=21 cm2=10.5 cmr = \frac{21 \text{ cm}}{2} = 10.5 \text{ cm} A=227×(10.5 cm)2=227×110.25 cm2A = \frac{22}{7} \times (10.5 \text{ cm})^2 = \frac{22}{7} \times 110.25 \text{ cm}^2
  2. Simplify and calculate the area.

    A=22×110.257 cm2=22×15.75 cm2A = 22 \times \frac{110.25}{7} \text{ cm}^2 = 22 \times 15.75 \text{ cm}^2 A=346.5 cm2A = 346.5 \text{ cm}^2

    The area of the circle is 346.5 cm2\boxed{\text{346.5 cm}^2}.

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