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Q.

From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1cm are removed. What is the area of the remaining sheet?

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a

30 sq. cm

b

20 sq.cm

c

100 sq.cm

d

536 sq.cm

answer is D.

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Detailed Solution

Given, from a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1cm are removed.
We know that

The area of a circle = π r^{2}

.
So,

the area of the circular plate = π \times 14^{2}

.

= 616

Therefore the total area of the circular plate is 616 sq. cm.
Removed area-
Two circles of radius 3.5cm are removed, rectangle of length 3 cm and breadth 1cm are removed.

The area of circles removed = 2 \times π \times {3.5}^{2}

=

77

The area of rectangle removed = (length \times breadth)

= (3 \times 1)

= 3
Therefore, the total area removed is 77 + 3= 80 sq. cm.
The area left in circular plate is 616 - 80= 536 sq. cm.
So option 4 is correct.

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