# Ex.12.2 Q10 Areas Related to Circles Solution - NCERT Maths Class 10

## Question

An umbrella has $$8$$ ribs which are equally spaced (see given figure). Assuming umbrella to be a flat circle of radius $$\text{45 cm,}$$ find the area between the two consecutive ribs of the umbrella.

Video Solution
Areas Related To Circles
Ex 12.2 | Question 10

## Text Solution

What is known?

An umbrella has $$8$$ ribs which are equally spaced. Assume umbrella to be a flat circle of radius $$= 45\,\rm{ cm.}$$

What is unknown?

The area between the $$2$$ consecutive ribs of the umbrella

Reasoning:

Since there are $$8$$ equal spaced ribs in an umbrella and the umbrella is assumed to be a flat circle.

$$\therefore \;$$Angle between $$2$$ consecutive ribs at the centre \begin{align}= \frac{{{{360}^o}}}{8} = {45^o}\end{align}

Area between $$2$$ consecutive ribs of the umbrella = Area of a sector with angle $$45^\circ$$

\begin{align}&= {\frac{\theta }{{{{360}^\circ }}} \times \pi {r^2}}\\& = {\frac{{{{45}^\circ }}}{{{{360}^\circ }}} \times \pi {r^2}}\\ &= {\frac{{\pi {r^2}}}{8}}\end{align}

Steps:

Since there are $$8$$ equally spaced ribs in the umbrella

$$\therefore$$ Angle between $$2$$ consecutive ribs $$\left( \theta \right)$$

\begin{align}&= \frac{{{{360}^\circ }}}{8}\\& = {45^\circ }\end{align}

Area between $$2$$ consecutive ribs of umbrella

\begin{align} &= {\frac{\theta }{{{{360}^\circ }}} \times \pi {r^2}}\\ &= {\frac{{{{45}^\circ }}}{{{{360}^\circ }}} \times \frac{{22}}{7} \times 45 \times 45}\\ &= {\frac{1}{8} \times \frac{{22}}{7} \times 45 \times 45}\\& = {\frac{{22275}}{{28}}{\text{c}}{{\text{m}}^2}}\\&{ = 795.535\,\,{\text{c}}{{\text{m}}^2}}\end{align}

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