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A wardrobe top is in the shape of a sector of a circle with radius 35 cm and angle 90 degrees. Calculate its perimeter.

Mathematics

ScanSolve AI Answer

Answer

125 cm\text{125 cm}

Step-by-step solution

2 steps

Let's calculate the perimeter of the wardrobe top.

The top of the wardrobe is a sector of a circle.
Given:
Radius r=35r = 35 cm
Angle θ=90∘\theta = 90^\circ
We will use π=227\pi = \frac{22}{7} for calculation.

  1. Calculate the length of the arc.

    The formula for the arc length LL of a sector is:

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

    Substitute the given values:

    L=90∘360∘×2×227×35 cmL = \frac{90^\circ}{360^\circ} \times 2 \times \frac{22}{7} \times 35 \text{ cm} L=14×2×227×35 cmL = \frac{1}{4} \times 2 \times \frac{22}{7} \times 35 \text{ cm} L=14×44×5 cmL = \frac{1}{4} \times 44 \times 5 \text{ cm} L=11×5 cmL = 11 \times 5 \text{ cm} L=55 cmL = 55 \text{ cm}
  2. Calculate the perimeter of the sector.

    The perimeter PP of a sector is the sum of the arc length and two radii:

    P=L+2rP = L + 2r

    Substitute the calculated arc length and the given radius:

    P=55 cm+2×35 cmP = 55 \text{ cm} + 2 \times 35 \text{ cm} P=55 cm+70 cmP = 55 \text{ cm} + 70 \text{ cm} P=125 cmP = 125 \text{ cm}

    The perimeter of the top of the wardrobe is 125 cm\text{125 cm}.

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