On a square cardboard sheet of area 784 cm² , four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates
Solution:
Given, four congruent circular plates of maximum size are placed on a square cardboard sheet of area 784 cm².
The circular plates are placed such that each plate touches the other two plates and each side of the square sheet is tangent to two circular plates.
We have to find the area of the square sheet not covered by the circular plates.
From the figure,
ABCD is a square sheet.
Given, area of square sheet = 784 cm²
Area of square = (side)²
784 = (side)²
Taking square root,
side = √784
side = 28 cm
Given, the four circular plates are congruent.
The diameter of each plate = 28/2 = 14 cm
Radius of each plate = 14/2 = 7 cm
Area of circle = πr²
Area of one circular plate = (22/7)(7)²
= 22(7)
= 154 cm²
Area of 4 congruent circular plates = 4(area of one circular plate)
= 4(154)
= 616 cm²
Area of the square sheet not covered by the plates = area of square - area of 4 circular plates.
= 784 - 616
= 168 cm²
Therefore, the area of the square sheet not covered by the circular plates is 168 cm².
✦ Try This: On a square cardboard sheet of area 400 cm² , four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 10
On a square cardboard sheet of area 784 cm² , four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates
Summary:
On a square cardboard sheet of area 784 cm², four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. The area of the square sheet not covered by the circular plates is 168 cm²
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