Symbiosis National Aptitude Test SNAP 2018 Paper

Question : 46 of 130

Marks: +1, -0

In the following diagram there are four semi circular arcs and a shaded region. The diameter of largest semi circle is 28 cm and of the smallest is 7 cm. The area of shaded region is ....

98.75π
120.5π
105.5π
110.25π

Validate

Solution:

Area of shaded region
= Area of semicircle of diameter AD + Area of semicircle of diameter BC - Area of two semicircle of diameter AB and CD.
From question, AD = 28 cm, AB = CD = 7 cm
BC = 28-7-7 = 14 cm
So, Area of shaded region
=

π[({28}/2)^2+({14}/2)^2-(7/2)^2-(7/2)^2]

π[196+49-{49}/2]

= 110.25π

cm^2

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