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10 grade maths

Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

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10 Months agoGrade
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1 Answer

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ApprovedApproved Tutor Answer10 Months ago

To find the area of a sector of a circle, we can use the relationship between the arc length, radius, and the angle of the sector. Here’s how to do it step by step:

Step 1: Identify the Given Values

  • Radius (r): 5 cm
  • Arc Length (L): 3.5 cm

Step 2: Calculate the Angle in Radians

The formula for arc length is:

L = r × θ

Where θ is the angle in radians. Rearranging this gives:

θ = L / r

Substituting the values:

θ = 3.5 cm / 5 cm = 0.7 radians

Step 3: Calculate the Area of the Sector

The area (A) of a sector can be calculated using the formula:

A = 0.5 × r² × θ

Now, substituting the known values:

A = 0.5 × (5 cm)² × 0.7

A = 0.5 × 25 cm² × 0.7 = 8.75 cm²

Final Result

The area of the sector is 8.75 cm².

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