If the wheel of a bicycle has a diameter of 60 cm, find how far a cyclist will have travelled after the wheel Class 9

If the wheel of a bicycle has a diameter of 60 cm, find how far a cyclist will have travelled after the wheel Class 9

Question 1.

If the wheel of a bicycle has a diameter of 60 cm, find how far a cyclist will have travelled after the wheel has rotated 100 times. Class 9

Solution:

Diameter of wheel = 60 cm

∴ r = $\frac{60}{2}$ = 30 cm

Number of rotations = 100

Distance in travelled by wheel one rotation = Circumference of circle

= 2πr

= 2 × $\frac{22}{7}$ × 30

= $\frac{44}{7}$ × 30 = $\frac{1320}{7}$ cm

∵ Total distance travelled by wheel in 100 rotations

= Distance by wheel in 1 rotation × 100

$\begin{aligned} & =\frac{1320}{7} \times 100 \\ & =\frac{132000}{7}\end{aligned}$

= 18857.14 cm = 188.57 m

∴ Distance travelled by wheel in 100 rotations

= 188.57 m.

Question 2.

Find the area of a quadrant of a circle whose circumference is 66cm. Class 9

Solution:

Given, Circumference of circle = 66 cm

∴ 2πr = 66

∴ 2 × $\frac{22}{7}$ × r = 66

∴ $\frac{44}{7}$ × r = 66

$\therefore \quad r=\frac{66 \times 7}{44}=10.5 \mathrm{~cm}$

Area of quadrant = $\frac{1}{4}$πr²

$\begin{aligned} \because \quad \text { Area of quadrant } & =\frac{1}{4} \times \frac{22}{7} \times(10.5)^2 \\ & =\frac{1}{4} \times \frac{22}{7} \times 10.5 \times 10.5 \\ & =\frac{1}{4} \times 22 \times 10.5 \times 1.5 \\ & =86.625\end{aligned}$

∴ Area of the quadrant = 86.63 cm²