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

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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