Question

From a circular sheet of radius 4 cm, a circle of radius 3 cm is cut out. Calculate the area of the remaining sheet after the smaller circle is removed.

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Answer 1

Answer:

Question :-

From a circular sheet of radius 4 cm, a circle of radius 3 cm is cut out. Calculate the area of the remaining sheet after the smaller circle is removed.

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$\huge \dag \mathbb \purple{ANSWER}$

Area of the circle with radius 4 cm = πr² = π(4)² = 16 π cm²

Area of the circle with radius 3 cm which is removed = π(3)² = 9π cm²

Remaining area = 16π - 9π = 7π = 7 x 3.14 = 21.98 cm²

• Thus, the area of the remaining sheet is 21.98 cm2.

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• Hopes it was helpful to you : )

Answer 2

Answer:

22cm²

Method

To calculate area of remaining sheet, we have to calculate the area of larger circle and smaller circle.

So let's calculate:-)

Step by Step Explanation

Calculating Area of Larger Circle

Radius = 4cm

Area = ?

$\:$

$\sf{Area_{[Circle]}=2πr²}$

$\:$

$\:$

$\sf{ \implies \: Area_{[Larger\:Circle]}= \dfrac{22}{7} \times (4)²}$

$\:$

$\implies\sf{Area_{[Larger \: Circle]}= \dfrac{22}{7} \times 16}$

$\:$

$\implies\sf{Area_{[Larger \: Circle]}= \dfrac{22 \times 16}{7} }$

$\:$

$\implies\sf{Area_{[Larger \: Circle]}= \dfrac{352}{7} }$

$\:$

$\sf{ \implies \: Area_{[Larger \: Circle]}=}50.28(approx)$

$\:$

Calculating Area of Smaller Circle

Radius = 3cm

Area = ?

$\sf{Area_{[Circle]}=2πr²}$

$\:$

$\sf{\implies \: Area_{[Smaller \: Circle]}= \dfrac{22}{7} \times( {3)}^{2}}$

$\:$

$\sf{\implies \: Area_{[Smaller \: Circle]}= \dfrac{22}{7} \times 9}$

$\:$

$\sf{\implies \: Area_{[Smaller \: Circle]}= \dfrac{22 \times 9}{7} }$

$\:$

$\sf{\implies \: Area_{[Smaller \: Circle]}= \dfrac{198}{7} }$

$\:$

$\sf{\implies \: Area_{[Smaller \: Circle]}=28.27(approx)}$

$\:$

$\:$

Calculating Area of the Remaining Sheet

$\sf{Area_{[Remaining \: Sheet]}=Area_{[Larger \: Sheet]}-Area_{[Smaller \: Sheet]}}$

$\:$

$\sf{Area_{[Remaining \: Sheet]}=50.27-28.27}$

$\:$

$\sf \pink {\underline{\boxed {\sf{Area_{[Remaining \: Sheet]}=22cm^{2}.}}}}$