Pls help me solve the above question

Mathematics

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Answer

50π3 cm2\frac{50\pi}{3} \text{ cm}^2

Step-by-step solution

6 steps

  1. Identify the given information.

    The question asks to find the area of a sector of a circle. The radius of the circle is given as r=10r = 10 cm, and the angle of the sector is θ=60∘\theta = 60^\circ.

  2. Recall the formula for the area of a sector.

    The area of a sector (AA) with radius rr and central angle θ\theta (in degrees) is given by:

    A=θ360∘×πr2A = \frac{\theta}{360^\circ} \times \pi r^2

  3. Substitute the given values into the formula.

    A=60∘360∘×π(10 cm)2A = \frac{60^\circ}{360^\circ} \times \pi (10 \text{ cm})^2

  4. Simplify the fraction and the radius term.

    A=16×π(100 cm2)A = \frac{1}{6} \times \pi (100 \text{ cm}^2)

  5. Perform the multiplication.

    A=100π6 cm2A = \frac{100\pi}{6} \text{ cm}^2

  6. Reduce the fraction to its simplest form.

    A=50π3 cm2A = \frac{50\pi}{3} \text{ cm}^2

    The area of the sector is 50π3 cm2\frac{50\pi}{3} \text{ cm}^2.

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