In Fig 11.4, a circle of radius 7.5 cm is inscribed in a square. Find the area of the shaded region (Use π = 3.14)
Solution:
Given, radius of circle inscribed in a square, r = 7.5 cm
We have to find the area of the shaded region.
Area of circle = πr²
= (3.14)(7.5)²
= 176.625 square cm.
Side of square = diameter of circle.
Diameter of circle = 2(7.5) = 15 cm
So, side of square = 15 cm
Area of square = (side)²
= (15)²
= 225 square cm
Area of shaded region = area of square - area of circle.
= 225 - 176.625
= 48.375 square cm.
Therefore, the area of the shaded region is 48.375 cm².
✦ Try This: In Fig, a circle of radius 5 cm is inscribed in a square. Find the area of the shaded region (Use π = 3.14)
Given, radius of circle inscribed in a square, r = 5 cm
We have to find the area of the shaded region.
Area of circle = πr²
= (3.14)(5)²
= 78.5 square cm.
Side of square = diameter of circle.
Diameter of circle = 2(5) = 10 cm
So, side of square = 10 cm
Area of square = (side)²
= (10)²
= 100 square cm
Area of shaded region = area of square - area of circle.
= 100 - 78.5
= 21.5 square cm.
Therefore, the area of the shaded region is 21.5 cm².
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.3 Sample Problem 3
In Fig 11.4, a circle of radius 7.5 cm is inscribed in a square. Find the area of the shaded region (Use π = 3.14)
Summary:
In Fig 11.4, a circle of radius 7.5 cm is inscribed in a square. The area of the shaded region is 48.375 square cm
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