EXERCISE 14.1

How many balls, each of radius$1 \mathrm{cm}$ can be made from a solid sphere of lead of radius$8 \mathrm{cm}?$

An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is $\frac{1}{\mathrm{4 }}$ of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.

A cylindrical bucket, $32 \mathrm{cm}$ high and with a radius of the base $18 \mathrm{cm}$ is filled with sand. This bucket is emptied out on the ground and a conical heap of sand is formed. If the height of the conical heap is $24 \mathrm{cm}$, find the radius and slant height of the heap. 

A solid metallic sphere of radius $5.6 \mathrm{cm}$ is melted and solid cones each of radius $2.8 \mathrm{cm}$ and height $3.2 \mathrm{cm}$ are made. Find the number of such cones formed.

A solid cuboid of iron with dimensions $53 \mathrm{cm}\times 40 \mathrm{cm}\times 15 \mathrm{cm}$ is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are $8 \mathrm{cm}$ and $7 \mathrm{cm}$, respectively. If the length (correct up to two places of decimal) of the pipe is $k$ $\mathrm{cm}$, then find $k$. (Take $\mathrm{\pi }=\frac{22}{7}$)

A hollow sphere of internal and external radii $2 \mathrm{cm}$ and $4 \mathrm{cm}$ respectively is melted into a cone of base radius $4 \mathrm{cm}$. Find the height and slant height of the cone.

A spherical ball of radius $3 \mathrm{cm}$ is melted and recast into three spherical balls. The radii of two of the balls are $1.5 \mathrm{cm}$ and $2 \mathrm{cm}$. If the diameter of the third ball is $k \mathrm{cm},$ then find $k$.

A cylindrical bucket, $32 \mathrm{cm}$ high and $18 \mathrm{cm}$ of the radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24 \mathrm{cm}$, find the radius and slant height of the heap.