A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that
space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is
(a) 142296
(b) 142396
(c) 142496
(d) 142596
Solution:
Internal edge of a hollow cube = 22 cm
Volume = (side)3 = (22)3 = 22 × 22 × 22 cm3 = 10648 cm3
Diameter of spherical marble = 0.5 cm =
In the given figure, the bottom of the glass has a hemispherical raised portion. If the glass is filled with orange juice, the quantity of juice which a person will get is
(a) 135 π cm3
(b) 117 π cm3
(c) 99 π cm3
(d) 36 π cm3
Solution:
Radius of base of cylinder (r) = cm = 3 cm
and height (h)= 15 cm
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