The volume of the largest right circular cone.

The volume of the largest right circular cone that can be carved out from a cube of edge 4.2 cm is
(a) 9.7 cm³
(b) 77.6 cm³
(c) 58.2 cm³
(d) 19.4 cm³

Solution:

Edge of cube = 4.2 cm
Radius of largest cone cut out = = 2.1 cm
and height = 4.2 cm
Volume =
= x × 2.1 × 2.1 × 4.2 cm³
= 19.404
= 19.4 cm³ (d)

The volume of the greatest sphere cut off from a circular cylindrical wood of base radius 1 cm and height 6 cm is
(a) 288 π cm³
(b) cm³
(c) 6 π cm³
(d) 4 π cm³

Solution:

Radius of cylinder (r) = 1 cm
Height (h) = 6 cm
The largest sphere that can be cut off from the cylinder of radius 1 cm

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