Derive the formula for the volume of the frustum of a conc, given to you in Section 13.5, using the symbols as explained.

The radii of the ends of a frustum of a cone 45 cm high are 28 cm and 7 cm (sec the given figure). Find the volume, the curved surface area and the total surface area (take pi=(22)/(7))

A fez, the cap used by the Turks, is shaped like the frustum of a cone (see the given figure). If its radius on the open side is 10 cm, radius at the upper side is 4 cm and its slant height is 15 cm, find the area of material used for making it.

Let us suppose you have two blocks and you do not know what material they are made of. The volume of one block is 30 cm^(3) while the other is 60 cm^(3). The second block is heavier than the first. Based on this information, can you tell which of the two blocks is denser?

For sound waves, the Doppler formula for frequency shift differs slightly between the two situations: (i) source at rest, observer moving, and (ii) source moving, observer at rest. The exact Doppler formulas for the case of light waves in vacuum are, however, strictly identical for these situations. Explain why this should be so. Would you expect the formulas to be strictly identical for the two situations in case of light travelling in a medium?

Estimate the volume of a water molecule using the data in Example 13.1.

The terminology different parts of the electromagnetic spectrum is given in the text. Use the formula E = hv (for energy of a quantum of radiation : photon) and obtain the photon energy in units of eV different parts of the electromagnetic spectrum. In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation ?

A solid toy isinthe form of a hemisphere surmounted by a right circular conc. The height of the cone is 2 cm and the diameter of the base is 4 cm . Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. (take pi=3.14) [ see the given figure)

An open metal bucket is in the shape of a frustum of a conce. Mounted on a hollow cylinderical base made of the same metallic sheet (see the given figure) the diameters of the two circular ends of the bucket are 45 cm and 25 cn. The vertical height of the bucket is 40 cm and that of the cylinderical base is 6 cm. find the area of the metallic sheet used to make the bucket, hwere we do not tak einto account the handle of the bucket. also, find the volu8me of water the bucket can hold (Take pi=(22)/(7))