Question

22. From a circular piece of cardboard of radius 1.47 m, a sector of angle 60° has been
removed. Find the area of the remaining cardboard.​

Answer 1

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Given:

A circular piece of cardboard having radius 1.47 m; a sector of 60° has been removed.

To find:

The area of the remaining cardboard.

Answer:

Let's first find the area of the cardboard.

Area of a circle = πr²

Area = π × (1.47)²

Area = 2.1609π m²

Now, let's find the area of the sector.

$\begin{gathered}\sf Area\ of\ a\ sector\ =\ \dfrac{\theta}{{360}^{\circ}}\ \times\ \pi\ \times\ r^2\\\\\\ \sf Area\ =\ \dfrac{{60}^{\circ}}{{360}^{\circ}}\ \times\ \pi\ \times\ (1.47)^2\\\\\\ \sf \: Area\ =\ \dfrac{1}{6}\ \times\ \pi\ \times\ 2.1609\\\\\\ \sf \: Area\ =\ 0.36015 \: \pi\ m^2\end{gathered}$

Area of the remaining portion = Area of the circle - Area of the sector.

Area of the remaining portion = 2.1609π - 0.36015π

Area of the remaining portion = 1.80075π

Area of the remaining portion = 5.654355 m²