R K Bansal Solutions for Exercise 1: EXERCISE

If the number of square centimeter on the surface of a sphere is equal to the number of cubic centimeter in its volume, what is the diameter of the sphere ?

A cubical block of side $7\mathrm{cm}$ is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.$\left(\mathrm{\pi }=\frac{22}{7}\right)$.

A vessel is in the form of an inverted cone. Its height is $8\mathrm{cm}$ and the radius of its top, which is open, is $5\mathrm{cm}.$ It is filled with water up to the rim. When lead shots, each of which is sa sphere of radius $0.5\mathrm{cm},$ are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.$\left(\mathrm{\pi }=\frac{22}{7}\right)$

A hemi-spherical bowl has negligible thickness and the length of its circumference is $198\mathrm{cm}.$ Find the capacity of the bowl.$\left(\mathrm{\pi }=\frac{22}{7}\right)$.

Find the maximum volume of a cone that can be craved out of a solid hemisphere of radius $r \mathrm{cm}.$ 

The radii of the bases of two solid right circular cones of same height are $r_{\mathit{1}}$ and $r_{\mathit{2}}$ respectively. The cones are melted and recast into a solid sphere of radius $\mathrm{R}.$ Find the height of each cone in terms of $r_{\mathit{1}}\mathit{ }\mathit{,}\mathit{ }{r}_{\mathit{2}}$ and $\mathrm{R}.$

A solid metallic hemisphere of diameter $28\mathrm{cm}$ is melted and recast into a number of identical solid cones, each of diameter $14\mathrm{cm}$ and height $8\mathrm{cm}.$ Find the number of cones so formed.$\left(\mathrm{\pi }=\frac{22}{7}\right)$

A cone and a hemisphere have the same base and the same height. Find the ratio between their volumes.