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CBSE Class 10 Standard Math 2026 All Sets Solved Paper

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Question : 14 of 20
Marks: +1, -0
Area of sector of a circle with radius 18 cm is 198 cm2198\ \mathrm{cm}^2. The measure of central angle is
Solution:  
Given: r = 18 cm, Area = 198 cm2198\ \mathrm{cm}^2
Area of Sector =   θ360∘×πr2\;\frac{\theta}{360^{\circ}} \times \pi r^2
198=  θ360∘×  227×18×18198 = \;\frac{\theta}{360^{\circ}} \times \;\frac{22}{7} \times 18 \times 18
198=  θ360∘×  227×324198 = \;\frac{\theta}{360^{\circ}} \times \;\frac{22}{7} \times 324
  198×722×324=  θ360∘\;\frac{198 \times 7}{22 \times 324} = \;\frac{\theta}{360^{\circ}}
  736=  θ360∘\;\frac{7}{36} = \;\frac{\theta}{360^{\circ}}
θ=  7×360∘36\theta = \;\frac{7 \times 360^{\circ}}{36}
θ=70∘\theta = 70^{\circ}
The measure of the central angle is 70°
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