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From a circular cylinder of diameter $14 cm$ and height $15 cm,$ a conical cavity of the same base radius and of the same height is hollowed out. What is the volume of the remaining solid taking $π = 227$ ?

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1600 cm 3

1500 cm 3

1640 cm 3

1540 cm 3

answer is D.

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Detailed Solution

Given that a circular cylinder of diameter

14 cm

and its height is

15 cm

.
We have the following formulae,
Volume of cone

= 13 π r 2 h

Volume of cylinder =

π r 2 h

Then,
r = 7cm
h = 15cm
Volume of the remaining solid will be,
Volume of the cylinder – volume of the cone

= π r 2 h − 13 π r 2 h = 23 π r 2 h = 23 × 227 × 7 × 7 × 15

= 1540 cm 3

Thus the volume of the remaining solid is

1540 cm 3

.
Therefore the correct option is 4.

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