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Calculate the area of a circle with radius 20cm, diameter 28cm, and area 145 cm2. Find its radius.

Mathematics

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let's calculate the areas and radii for these circles!

The formula for the area of a circle is A=πr2A = \pi r^2, where rr is the radius. We will use π=227\pi = \frac{22}{7} as shown in the examples.

1. Calculate the area of a circle of radius 20cm.

  1. Identify the given radius.

    r=20 cmr = 20 \text{ cm}
  2. Apply the area formula.

    A=πr2A = \pi r^2 A=227×(20 cm)2A = \frac{22}{7} \times (20 \text{ cm})^2 A=227×400 cm2A = \frac{22}{7} \times 400 \text{ cm}^2 A=88007 cm2A = \frac{8800}{7} \text{ cm}^2
  3. Calculate the numerical value.

    A≈1257.14 cm2A \approx 1257.14 \text{ cm}^2

    The area of the circle is 1257.14 cm2\boxed{\text{1257.14 cm}^2}.

    2. Find the area of a circle whose diameter is 28cm.

  4. Determine the radius from the given diameter.

    d=28 cmd = 28 \text{ cm} r=d2=28 cm2=14 cmr = \frac{d}{2} = \frac{28 \text{ cm}}{2} = 14 \text{ cm}
  5. Apply the area formula.

    A=πr2A = \pi r^2 A=227×(14 cm)2A = \frac{22}{7} \times (14 \text{ cm})^2 A=227×196 cm2A = \frac{22}{7} \times 196 \text{ cm}^2
  6. Simplify the expression.

    A=22×28 cm2A = 22 \times 28 \text{ cm}^2 A=616 cm2A = 616 \text{ cm}^2

    The area of the circle is 616 cm2\boxed{\text{616 cm}^2}.

    3. The area of a circle whose is 145cm. Calculate its radius.
    (Assuming the question means "The area of a circle whose area is 145 cm2^2")

  7. Identify the given area.

    A=145 cm2A = 145 \text{ cm}^2
  8. Use the area formula to solve for the radius.

    A=πr2A = \pi r^2 145 cm2=227r2145 \text{ cm}^2 = \frac{22}{7} r^2
  9. Isolate r2r^2 and then solve for rr.

    r2=145×722 cm2r^2 = \frac{145 \times 7}{22} \text{ cm}^2 r2=101522 cm2r^2 = \frac{1015}{22} \text{ cm}^2 r=101522 cmr = \sqrt{\frac{1015}{22}} \text{ cm}
  10. Calculate the numerical value.

    r≈46.136 cmr \approx \sqrt{46.136} \text{ cm} r≈6.79 cmr \approx 6.79 \text{ cm}

    The radius of the circle is 6.79 cm\boxed{\text{6.79 cm}}.

    4. The diameter of the clock face on a town hall is 30cm. Find area of the clock face to the 1 cm.

  11. Determine the radius from the given diameter.

    d=30 cmd = 30 \text{ cm} r=d2=30 cm2=15 cmr = \frac{d}{2} = \frac{30 \text{ cm}}{2} = 15 \text{ cm}
  12. Apply the area formula.

    A=πr2A = \pi r^2 A=227×(15 cm)2A = \frac{22}{7} \times (15 \text{ cm})^2 A=227×225 cm2A = \frac{22}{7} \times 225 \text{ cm}^2
  13. Calculate the numerical value and round to the nearest whole number.

    A=49507 cm2A = \frac{4950}{7} \text{ cm}^2 A≈707.14 cm2A \approx 707.14 \text{ cm}^2

    Rounding to the nearest 1 cm2^2:

    A≈707 cm2A \approx 707 \text{ cm}^2

    The area of the clock face is 707 cm2\boxed{\text{707 cm}^2}.

    5. Find the area of the circular web of a spider if the radius is 1.4cm.

  14. Identify the given radius.

    r=1.4 cmr = 1.4 \text{ cm}
  15. Apply the area formula.

    A=πr2A = \pi r^2 A=227×(1.4 cm)2A = \frac{22}{7} \times (1.4 \text{ cm})^2 A=227×1.96 cm2A = \frac{22}{7} \times 1.96 \text{ cm}^2
  16. Simplify the expression.

    A=22×0.28 cm2A = 22 \times 0.28 \text{ cm}^2 A=6.16 cm2A = 6.16 \text{ cm}^2

    The area of the circular web is 6.16 cm2\boxed{\text{6.16 cm}^2}.

    6. What is the area of a circle of radius 3.5cm?

  17. Identify the given radius.

    r=3.5 cmr = 3.5 \text{ cm}
  18. Apply the area formula.

    A=πr2A = \pi r^2 A=227×(3.5 cm)2A = \frac{22}{7} \times (3.5 \text{ cm})^2 A=227×(72)2 cm2A = \frac{22}{7} \times \left(\frac{7}{2}\right)^2 \text{ cm}^2
  19. Simplify the expression.

    A=227×494 cm2A = \frac{22}{7} \times \frac{49}{4} \text{ cm}^2 A=22×74 cm2A = \frac{22 \times 7}{4} \text{ cm}^2 A=1544 cm2A = \frac{154}{4} \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}.

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