Exercise 13.3

Metallic spheres of radii $6 \mathrm{c}\mathrm{m},8 \mathrm{c}\mathrm{m}$ and $10 \mathrm{c}\mathrm{m}$ respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

A $20 \mathrm{m}$ deep well with diameter $7 \mathrm{m}$ is dug and the earth from digging is evenly spread out to form a platform $22 \mathrm{m}$ by $14 \mathrm{m}$. Find the height of the platform.

A well of diameter $3 \mathrm{m}$ is dug $14 \mathrm{m}$ deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width $4 \mathrm{m}$ to form an embankment. Find the height of the embankment.

A container shaped like a right circular cylinder having diameter $12 \mathrm{c}\mathrm{m}$ and height $15 \mathrm{c}\mathrm{m}$ is full of ice cream. The ice cream is to be filled into cones of height $12 \mathrm{c}\mathrm{m}$ and diameter $6 \mathrm{c}\mathrm{m}$, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

How many silver coins, $1.75 \mathrm{c}\mathrm{m}$ in diameter and of thickness $2 \mathrm{m}\mathrm{m}$, must be melted to form a cuboid of dimensions $5.5 \mathrm{c}\mathrm{m}\times 10 \mathrm{c}\mathrm{m}\times 3.5 \mathrm{c}\mathrm{m}$?

A cylindrical bucket, $32 \mathrm{c}\mathrm{m}$ high and with radius of base $18 \mathrm{c}\mathrm{m}$, 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 $24 \mathrm{c}\mathrm{m}$, find the radius and slant height of the heap.

Water in a canal, $6 \mathrm{m}$ wide and $1.5 \mathrm{m}$ deep, is flowing with a speed of $10 \mathrm{k}\mathrm{m}/\mathrm{h}$. How much area will it irrigate in $\mathrm{}30$ minutes, if $8 \mathrm{c}\mathrm{m}$ of standing water is needed?

A farmer connects a pipe of internal diameter $20 \mathrm{c}\mathrm{m}$ from a canal into a cylindrical tank in her field, which is $10 \mathrm{m}$ in diameter and $2 \mathrm{m}$ deep. If water flows through the pipe at the rate of $3 \mathrm{k}\mathrm{m}/\mathrm{h}$, in how much time will the tank be filled ?