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Calculate the area of a sector with radius 21 cm and angle 90 degrees, using pi = 22/7.

Mathematics

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Answer

346.5 cm2\text{346.5 cm}^2

Step-by-step solution

4 steps
  1. Identify the given values for the sector.

    The radius of the sector is r=21 cmr = 21 \text{ cm}.
    The angle of the sector is θ=90∘\theta = 90^\circ.
    We are given to use π=227\pi = \frac{22}{7}.

  2. Write down the formula for the area of a sector.

    The area of a sector is given by the formula:

    A=θ360∘×πr2A = \frac{\theta}{360^\circ} \times \pi r^2
  3. Substitute the given values into the formula.

    A=90∘360∘×227×(21 cm)2A = \frac{90^\circ}{360^\circ} \times \frac{22}{7} \times (21 \text{ cm})^2
  4. Simplify the expression and calculate the area.

    First, simplify the fraction 90∘360∘\frac{90^\circ}{360^\circ}:

    90∘360∘=14\frac{90^\circ}{360^\circ} = \frac{1}{4}

    Next, calculate (21 cm)2(21 \text{ cm})^2:

    (21 cm)2=441 cm2(21 \text{ cm})^2 = 441 \text{ cm}^2

    Now, substitute these back into the area formula:

    A=14×227×441 cm2A = \frac{1}{4} \times \frac{22}{7} \times 441 \text{ cm}^2 A=14×22×4417 cm2A = \frac{1}{4} \times 22 \times \frac{441}{7} \text{ cm}^2 A=14×22×63 cm2A = \frac{1}{4} \times 22 \times 63 \text{ cm}^2 A=22×634 cm2A = \frac{22 \times 63}{4} \text{ cm}^2 A=13864 cm2A = \frac{1386}{4} \text{ cm}^2 A=346.5 cm2A = 346.5 \text{ cm}^2

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

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