Question

From a rectangular piece of metal sheet,
with length and breadth
equal to 1.60m and 80 cm, respectively, 3 circular sheets of 21
cm radius 3 each are cut out. Find the area of the remaining
sheet.​

Answer 1

Answer:

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Answer 2

Question :

From a rectangular piece of metal sheet, with length and breadth equal to 1.60m and 80 cm, respectively, 3 circular sheets of 21 cm radius each are cut out. Find the area of the remaining sheet.

Given :

• Length of Rectangular metal sheet = 1.60m.
• Breadth of the Rectangular metal sheet = 80cm.
• The circles of Radius 21 cm cut out from the rectangular metal sheet.

To Find :

• Area of remaining Metal sheet.

Explanation :

Its guven that in the rectangular metal sheet of length 1.60m and breadth 80cm. Three circles of radius 21cm have been cut out. Now we have to find the area of remaining metal sheet. We cab find the area of remaining metal sheet by following steps.

1. Find the area of rectangle.
2. Find area of Circle.
3. Reduce the area of circles from the area of rectangle.

Formula Applied :

$\sf\underline{\boxed{\sf Area_{(Remaining \:sheet)}= Area_{(Rectangle)}-3 \times Area _{(Circle)}}}$

• $\sf{Area\:of\:Rectangle= l \times b}$
• $\sf{Area\:of\:Circle= \pi r^2 }$

Solution :

1.Area Of Rectangle :

• Before Substituting the given values in the formula change all measurement to same units (Centimetres)

$\sf \boxed{\sf 1\:m = 100\:cm}$

$\sf \implies 1.60\:m = 160\:cm$

$\sf{Area\:of\:Rectangle= l \times b}$

$\sf \implies 160 \times 80$

$\sf \implies 12,800$

$\sf \boxed{\sf Area\:of\:Rectangle= 12,800\:cm^2}$

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2. Area Of Square :

$\sf{Area\:of\:Circle= \pi \times r^2 }$

$\displaystyle {\sf \implies \frac{22}{7}\times 21 \times 21}$

$\displaystyle {\sf \implies 22 \times 21 \times 3 }$

$\displaystyle {\sf \implies 1386\:cm^2 }$

$\sf \boxed{\sf Area\:of\:Circle= 1,386\:cm^2}$

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3. Area Of Remaining Sheet :

$\sf{Area_{(Remaining \:sheet)}= Area_{(Rectangle)}-3 \times Area _{(Circle)}}$

$\sf\implies 12,800-3 \times1386$

$\sf\implies 12,800-4158$

$\sf\implies 8642$

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Required Answer :

Area of the remaining Rectangular metal sheet is $\sf \underline{8642\: cm^2 }$