M L Aggarwal Solutions for Exercise 5: Exercise 17.5

A solid metallic sphere of radius $6 \mathrm{cm}$ is melted and made into a solid cylinder of height $32 \mathrm{cm}$. Find the radius of the cylinder.

Two spheres of the same metal weigh $1 \mathrm{kg}$ and $7 \mathrm{kg}$. The radius of the smaller sphere is $3 \mathrm{cm}$. The two spheres are melted to form a single big sphere. Find the diameter of the big sphere.

A hollow copper pipe of inner diameter $6 \mathrm{cm}$ and outer diameter $10 \mathrm{cm}$ is melted and changed into a solid circular cylinder of the same height as that of the pipe. Find the diameter of the solid cylinder.

A cylindrical can of internal diameter $21 \mathrm{cm}$ contains water. A solid sphere whose diameter is $10.5 \mathrm{cm}$ is lowered into the cylindrical can. The sphere is completely immersed in water. Calculate the rise in water level, assuming that no water overflows.

A vessel in the form of an inverted cone is filled with water to the brim. Its height is $20 \mathrm{cm}$ and diameter is $16.8 \mathrm{cm}$. Two equal solid cones are dropped in it so that they are fully submerged. As a result, one third of the water in the original cone overflows. What is the volume of each of the solid cone submerged?

A solid metallic circular cylinder of radius $14 \mathrm{cm}$ and height $12 \mathrm{cm}$ is melted and recast into small cubes of edge $2 \mathrm{cm}$. How many such cubes can be made from the solid cylinder?

A solid metal cylinder of radius $14 \mathrm{cm}$ and height $21 \mathrm{cm}$ is melted down and recast into spheres of radius $3.5 \mathrm{cm}$. Calculate the number of spheres that can be made.

The surface area of a solid metallic sphere is $1256 c{m}^2$. It is melted and recast into solid right circular cones of radius $2.5 cm$ and height $8 cm$. Calculate the number of cones recast .$($Use $\mathrm{\pi }=3.14)$