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9.A solid is in the shape of a cone standing on a hemisphere with both their radii being equal
to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in
terms of π.

10. Rachel, an engineering student, was asked to make a model shaped like a cylinder with
two cones attached at its two ends by using a thin aluminium sheet. The diameter of the
model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of
air contained in the model that Rachel made. (Assume the outer and inner dimensions of
the model to be nearly the same.)

11. A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately
how much syrup would be found in 45 gulabl jamuns, each shaped like a cylinder with two
hemispherical ends with length 5 cm and diameter 2.8 cm (see figure).

12. A pen stand made of wood is in the shape of a cuboid with four conical depressions to
hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each
of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire
stand (see Fig.).

13. A vessel is in the form of an inverted cone. its height is 8 cm and the radius of its top,
which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which
is a sphere of radius 0.5 cm are dropped into the vessel, one-forth of the water flows out.
Find the number of lead shots dropped in the vessel.

14. A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which
is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the
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pole, given that 1 cm of iron has approximately 8 g mass.

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