CAT Practice : Mensuration

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This question requires a bit of visualization and the ability to express one area in terms of another.

Circles

Q.12: PQRS is a circle and circles are drawn with PO, QO, RO and SO as diameters areas A and B are shaded A/B is equal to

1. ${\pi}$
2. 1
3. ${\frac{\pi}{4}}$
4. 2

Choice B. 1

Detailed Solution

Diagram -

Such questions are all about visualization and ability to write one area in terms of others.

Here,

Let the radius of PQRS be 2r

∴ Radius of each of the smaller circles = ${\frac{2r}{2}}$ = r

∴ Area A can be written as

A = π (2r)2 – 4 x π(r)2 (Area of the four smaller circles) + B (since, B has been counted twice in the previous subtraction)

=) A = 4πr2 - 4πr2 + B

=) A = B

=) ${\frac{A}{B}}$ = 1

Choice (B) is therefore, the correct answer.

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Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.