An umbrella has $8$ ribs which are equally spaced (see $Fig.$). Assuming the umbrella to be a flat circle of radius $45 \, cm ,$ find the area between the two consecutive ribs of the umbrella. [use $\pi=\frac{22}{7}$]

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) An umbrella has $8$ ribs,which divide the circular area into $8$ equal sectors.
The angle subtended by each sector at the center is $\theta = \frac{360^{\circ}}{8} = 45^{\circ}$.
The radius of the circle is $r = 45 \, cm$.
The area of a sector is given by the formula: $\text{Area} = \frac{\theta}{360^{\circ}} \times \pi r^{2}$.
Substituting the values:
$\text{Area} = \frac{45^{\circ}}{360^{\circ}} \times \frac{22}{7} \times (45)^{2}$
$\text{Area} = \frac{1}{8} \times \frac{22}{7} \times 2025$
$\text{Area} = \frac{11}{4 \times 7} \times 2025 = \frac{11 \times 2025}{28}$
$\text{Area} = \frac{22275}{28} \, cm^{2} \approx 795.54 \, cm^{2}$.

Explore More

Similar Questions

The length of the minute hand of a clock is $14 \, cm$. Find the area swept by the minute hand in $5 \, minutes$. [use $\pi = \frac{22}{7}$]

From each corner of a square of side $4\, cm$,a quadrant of a circle of radius $1\, cm$ is cut and also a circle of diameter $2\, cm$ is cut as shown in the figure. Find the area of the remaining portion of the square. [Use $\pi = \frac{22}{7}$]

The radii of two circles are $19\, cm$ and $9\, cm$ respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. (in $cm$) [use $\pi=\frac{22}{7}$]

Find the area of the shaded region in the figure,where a circular arc of radius $6 \, cm$ has been drawn with vertex $O$ of an equilateral triangle $OAB$ of side $12 \, cm$ as centre. $\left[ \text{Use } \pi = \frac{22}{7} \right]$

Difficult
View Solution

In the given figure,$OACB$ is a quadrant of a circle with centre $O$ and radius $3.5 \, cm$. If $OD = 2 \, cm$,find the area of the:
$(i)$ quadrant $OACB$,
$(ii)$ shaded region. $\left[ \text{Use } \pi = \frac{22}{7} \right]$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo