cylinder = HP = BO = cm, and its height is EH = AO + OP = ( + ) cm = cm So, the volume required = volume of the right circular cylinder – volume of the toy = ( . × × – . ) cm = . cm Hence, the required difference of the two volumes = .
cm . EXERCISE . Unless stated otherwise, take = . A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to cm and the height of the cone is equal to its radius.
Find the volume of the solid in terms of . . 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 cm and its length is cm.
If each cone has a height of 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.) Fig. . .
A gulab jamun, contains sugar syrup up to about % of its volume. Find approximately how much syrup would be found in gulab jamuns, each shaped like a cylinder with two hemispherical ends with length cm and diameter . cm (see Fig. .
). . 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 cm by cm by .
cm. The radius of each of the depressions is . cm and the depth is . cm.
Find the volume of wood in the entire stand (see Fig. . ). .
A vessel is in the form of an inverted cone. Its height is cm and the radius of its top, which is open, is cm. It is filled with water up to