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Mensuration - Area

Multiple Choice Questions

111.

A square ABCD is inscribed in a circle of unit radius. Semi-circles are described on each side as a diameter. The area of the region bounded by the four semi-circles and the circle is

1 sq unit
2 sq unit
1.5 sq unit
2.5 sq unit

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112.

The sides of a triangle having area 7776 sq cm are in the ratio 3 : 4 : 5. The Perimeter of the triangle is

412 cm
424 cm
400 cm
432 cm

113.

If the area of a circle is A, radius of the circle is r and circumference of it is C, then

rC = 2A
$straight A over straight r space equals space straight C$
$AC space equals space straight r squared over 4$
$straight C over straight A space equals space straight r over 2$

114.

The perimeter of one face of a cube is 20 cm. Its volume will be

400 cm³
125 cm³
625 cm³
100 cm³

115.
A solid sphere of diameter 17.5 cm is cut into two equal halves. What will be the increase (in cm²) in the total surface area?

289 cm²

361.5 cm²

481.25 cm²

962.5 cm²

481.25 cm²

Since the sphere is cut into two equal halves, we will get two hemispheres.
Total Surface area of both hemispheres = $2 space cross times space 3 πr squared space equals space 6 πr squared$
Total Surface area of solid sphere = $4 πr squared$
∴ Increase in total surface area $equals space 6 πr squared space minus space 4 πr squared space equals space 2 πr squared$
$equals space 2 space cross times space 22 over 7 space cross times space open parentheses fraction numerator 17.5 over denominator 2 end fraction close parentheses squared equals space 481.25 space cm squared$