Three cubes with sides in the ratio $3:4:5$ are melted to form a single cube whose diagonal is $12\sqrt{3} \mathrm{cm}$. The sides of the cube, respectively, are

The radius and height of the cylinder are in the ratio $5:7$ and its volume is $550 {\mathrm{cm}}^3$. Find its radius and height.

How many soap cakes each measuring $7 \mathrm{cm}\times 5 \mathrm{cm}\times 2.5 \mathrm{cm}$ can be placed in a box of size $56 \mathrm{cm}\times 40 \mathrm{cm}\times 25 \mathrm{cm}$?

A cuboidal fish tank $91 \mathrm{cm}$long, $66 \mathrm{cm}$ wide and $60 \mathrm{cm}$ deep is filled with water to the brim. Water from the tank is emptied with the help of a cylindrical container of diameter $14 \mathrm{cm}$ and height $15 \mathrm{cm}.$ How many containers of water are removed to empty the tank?

The ratio of the radii of two cylinders is $2:3$ and the ratio of their heights is $5:3$. Find the ratio of their volumes.

Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:

Length $=22 \mathrm{cm}$, Breadth $=12 \mathrm{cm}$ and Height $=7.5 \mathrm{cm}$

Find the number of coins, $1.5 \mathrm{cm}$ in diameter and $0.2 \mathrm{cm}$ thick, to be melted to form a right circular cylinder with a height of $10 \mathrm{cm}$ and a diameter of $4.5 \mathrm{cm}$.

Find the volume of the following solid.

A cube of side $11 \mathrm{cm}$.

Three cubes of edges $x cm, 4 cm$and $5 cm$ are melted and shaped into a large cube of edge $6 cm.$ Then the value of $x$ is:

(Note : none of the options given in the textbook was correct. So, one of the options is changed accordingly.)

Find the volume of a cube whose total surface area is $384 {\mathrm{cm}}^2$.