Question

A circle with radius of 3 cm sits inside a circle with radius of 11 cm. What is the area of the shaded region?

Answer 1

Answer:

The area of shaded region is 351.68 cm².

Step-by-step explanation:

$\sf{\underline{\underline{Given :}}}$

• ➝ Radius of small circle = 3 cm
• ➝ Radius of big circle = 11 cm

$\sf{\underline{\underline{To \: Find:}}}$

• ➝ Area of small circle
• ➝ Area of big circle
• ➝ Area of shaded region

$\sf{\underline{\underline{Using\: Formula :}}}$

• ➝ Area of small circle = πr²
• ➝ Area of big circle = πR²
• ➝ Area of shaded region = Area of small circle - Area of big circle

$\sf{\underline{\underline{Solution :}}}$

Finding the area of small circle by substituting the values in the formula :

• $\red\implies$ Area of small circle = πr²
• $\red\implies$ 3.14 × 3²
• $\red\implies$ 3.14 × 3 × 3
• $\red\implies$ 28.26cm²

Hence, the area of small circle is 28.26cm².

$\rule{200}2$

Finding the area of big circle by substituting the values in the formula :

• $\pink\implies$ Area of big circle = πR²
• $\pink\implies$ 3.14 × 11²
• $\pink\implies$ 3.14 × 11 × 11
• $\pink\implies$ 379.94cm²

Hence, the area big circle is 379.94cm².

$\rule{200}2$

Finding the area of shaded region by substituting the values in the formula :

• $\orange\implies$ Area of shaded region = Area of bigger circle - Area of smaller circle
• $\orange\implies$ 379.94 - 28.26 cm²
• $\orange\implies$ 351.68 cm²

Hence, the area of shaded region is 351.68 cm².

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