A lamp shade is in the shape of a part of a cone and its top and bottom ends are circles whose circu...........

Quantitative Aptitude (CDS) Mensuration 2D

A lamp shade is in the shape of a part of a cone and its top and bottom ends are circles whose circumferences are respectively 30 cm and 40 cm. The perpendicular distance between the ends is 6 cm. If the cone were to be completed, then how far would its vertex be from the top end ?

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2023 CDS -2 MATH

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20 cm

18 cm

12 cm

9 cm

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Explanation:

Correct option 2: 18 cm

Given:
Circumferences of top and bottom are 30 cm & 40 cm respectively.
The perpendicular distance between the ends is 6 cm.
Solution

Here, Ratio of circumference = ST: PQ = 3:4 We know that, Circumference << Radius Therefore, AOST~ AOPQ
⇒OS: OP = 3:4
We know that, SP = 1 unit = 6 cm
⇒ OS = 3 unit = 6 x 3 = 18 cm
The distance of its vertex from the top is 18 cm.