Question

The figure below shows three small circles, each with a diameter of 6 centimeters, inside a larger circle. What is the area of the shaded part of the figure?

Answer 1

Given that,

• The diameter of the Smaller circle is 6cm.
• And, The diameter of the Bigger circle is 18cm [6 + 6 + 6 = 18].

To Find,

• The Area of Shaded Region.

Solution,

As given,

• The diameter ( d ) of the Smaller circle = 6cm

We found,

• The radius ( r ) of the Smaller circle is 3cm [6/2 = 3]. •••[1]

As given,

• The diameter ( D ) of the Bigger circle = 18cm

We found,

• The radius ( R ) of the Bigger circle is 9cm [18/2 = 9]. •••[2]

As given in figure,

• •➤ Area of Shaded Region = Area of Bigger Circle - Area of Smaller Circles
• •➤ Area of Shaded Region = π R² - 3(π r²)
• •➤ Area of Shaded Region = π (R² - 3r²)

By Equation [1] and [2],

• •➤ Area of Shaded Region = π [9² - 3(3²)]
• •➤ Area of Shaded Region = π [81 - 3(9)]
• •➤ Area of Shaded Region = π (81 - 27) cm²
• •➤ Area of Shaded Region = 22/7 × 54 cm²
• •➤ Area of Shaded Region = 169.71cm²

Hence, The Area of Shaded Region is 169.71 cm².

Required Answer,

• The Area of Shaded Region is 169.71 square cms.

Answer 2

the answer is 216

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