NCERT Class 10 Math Chapter 11 Important Questions Answer – Areas Related to Circles

Class 10
Chapter  Areas Related to Circles
Subject Math
Category Important Question Answer

Class 10 Math Chapter 11 Important Question Answer

Q1. Find the area of the sector of a circle with radius 7 cm and the angle at the centre is 30°.  Most Most Important

Ans. Given r = 7cm, θ = 30°

Area of sector =  \displaystyle \frac{\theta }{{360}}\times 2\pi r

=  \displaystyle \frac{{30}}{{360}}\times 2\times \frac{{22}}{7}\times 7=\frac{{77}}{6} cm2

Q2. A chord of a circle of radius 10 cm subtends an angle of 60° at the centre. Find the area of the corresponding sector.

Ans. Given r = 10 cm, θ = 60°

Area of sector =  \displaystyle \frac{\theta }{{360}}\times \pi {{r}^{2}}

=  \displaystyle \frac{{60}}{{360}}\times \frac{{22}}{7}\times 10\times 10 =  \displaystyle \frac{{1100}}{{21}} cm2

Q3. The circumference of semi-circular piece of design is 72 cm. Find its area.

Ans. Given, Circumference of a semi-circle = 72 cm, area of semicircle = ?

Using, Circumference of a semi-circle = 2r + πr

By comparing,

2r + πr = 72

r(2 + π) = 72

 \displaystyle r\left( {\frac{{36}}{7}} \right)=72

r = 14 cm

Area of semicircle =  \displaystyle \frac{{\pi {{r}^{2}}}}{2}

=  \displaystyle \frac{1}{2}\left( {\frac{{22}}{7}\times 14\times 14} \right)=308 cm2

Q4. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the length of arc.

Ans. Given r = 21 cm, θ = 60°

Length of arc =  \displaystyle \frac{\theta }{{360}}\times 2\pi r

=  \displaystyle \frac{{60}}{{360}}\times 2\times \frac{{22}}{7}\times 21=22 cm

Q5. Circumference of a circle is 22 cm, find the radius of the circle.

Ans. Given circumference of a circle = 22 cm

Using, Circumference of a circle = 2r

On comparing,

2πr = 22

 \displaystyle 2\times \frac{{22}}{7}\times r = 22

r =  \displaystyle \frac{7}{2} cm

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