Question

38. From each corner of a rectangular paper (30 cm x 20 cm) a quadrant of a circle of
radius 7 cm is cut. Find the area of the remaining paper i.e., shaded portion
7 cm
7 cm
7 cm
20 cm
7 cm
30 cm​

Answer 1

AnswEr :

Area of shaded portion is 446 cm².

We're provided with the information that each corner of a rectangular paper (30 cm × 20 cm) a quadrant of a circle of radius 7 cm is cut. And we've to find the area of shaded region.

GiveN:

• Radius of the circle = 7 cm

• Dimensions = 30 cm × 20 cm

Firstly, we'll calculate the area of rectanglular paper & then area of the 1 quadrant. To find the area of shaded portion we'll subtract area of rectanglular paper & area of 4 quadrants respectively.

Likewise, let's calculate the Area of rectangular paper now !

$\longrightarrow$ Area of rectanglular paper = length × Breadth

$\longrightarrow$ Area of rectanglular paper = 30 cm × 20 cm

$\longrightarrow$ Area of rectanglular paper = 600 cm².

Now,

$\longrightarrow$ Area of 1 quadrant = $\sf \dfrac{1}{4}$ × πr²

$\longrightarrow$ Area of 4 quadrants = 4 × $\sf \dfrac{1}{4}$ × $\sf \dfrac{22}{7}$ × 7²

$\longrightarrow$ Area of 4 quadrants = $\sf \dfrac{22}{7}$ × 7²

$\longrightarrow$ Area of 4 quadrants = 154 cm².

Further,

$\longrightarrow$ Area of shaded portion = Area of rectanglular paper - Area of 4 quadrants

$\longrightarrow$ Area of shaded portion = 600 - 154

$\longrightarrow$ Area of shaded portion = 446 cm².