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What will be the approximate volume of the largest right circular cone that can be cut out from a cube of edge $4.2 cm ?$

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18.40 cm 3

19.40 cm 3

19.20 cm 3

17.10 cm 3

answer is B.

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Detailed Solution

Given that the edge is

4.2 cm

We have the following formula,
Volume of cone will be

= 13 π r 2 h

Then the diameter of largest circular cone that can be formed will be

4.2 cm

.
Considering the radius at base of the cone as r cm,
Height = h cm.
We have,
2r = 4.2 cm
r = 2.1 cm
The size of edge will be the height of the cone,
h = 4.2 cm
Volume of cone will be,

= 13 × 227 × 2.1 × 2.1 × 4.2 = 19.40 cm 3

Thus, the volume is

19.40 cm 3

.
Therefore the correct option is 2.

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