11. From a square cardboard of area 196 cm', a circle
with biggest area is cut out. Find the area of the
remaining cardboard
Answers
Answer:
Area of the remaining cardboard is 42cm
2
Step-by-step explanation:
Side of square =
Area
=
196
=14
Diameter of circle with largest possible are a cut out from square = side of square
d=14
r=
2
d
=7cm
Area of circle πr
2
=
7
22
×7×7
=154cm
2
Area of Remaining board = Area of square - Area of circle
=196−154
=42cm
2
I hope it will help you.
Answer:
Area of remaining carboard = 42 cm²
Step-by-step explanation:
Given:
- Area of square = 196 cm²
To Find:
- Area of the remaining carboard when a circle with the biggest area is cut out.
Concept:
First find the side of the square. Now find the area of the largest circle possible and subtract it from the area of the square to get the area of the remaining carboard.
Solution:
First we have to find the side of the square.
We know that area of a square is given by,
Area of a square = a × a
where a is a side of the square.
Substituting the data,
a² = 196
a = √196
a = 14 cm
Hence side of the square is 14 cm.
Now it is given that a circle with largest area is cut out.
Hence,
Diameter of circle = Side of square
Diameter of circle = 14 cm
Radius of circle = 14//2 = 7 cm.
Now we have to find the area of the circle.
Area of a circle is given by,
Area of a circle = π r²
Substitute the data,
Area of circle = 22/7 × 7 × 7
Area of circle = 22 × 7 = 154 cm²
Hence area of circle is 154 cm²
Now,
Area of remaining carboard = Area of square - Area of circle
Hence,
Area of remaining carboard = 196 - 154
Area of remaining carboard = 42 cm²
Hence area of the remaining carboard is 42 cm².