Geometry & Mensuration
Aptitude

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Q.

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.

Image for Mensuration, Aptitude:2167-1

 A.

104.22 cm\(^3\)

 B.

 162.08 cm\(^3\)

 C.

 427.56 cm\(^3\)

 D.

 266.11 cm\(^3\)

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Solution:
Option(D) is correct

Volume of the cone is given by

\(=\dfrac{1}{3}\times \pi r^2 h\)

Here \(r=4.2\) cm, \(h=10.2-r=6\) cm

Therefore, the volume of the cone

\(=\dfrac{1}{3}\pi\times 4.2^2\times 6\)

\(=110.88\text{ cm}^3\)

Volume of the hemisphere

\(=\dfrac{1}{2}\times \dfrac{4}{3}\pi r^3\)

\(=155.23\)

Total volume

\(=110.88+155.232\)

\(=266.112\)


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Swapnil
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Quadrilateral ABCD is circumscribed about a circle. If the length of AB, BC, CD are 7cm, 8.5 cm and 9.2cm respectively, then the length (in cm) of DA is