Volume of Cube and Cuboid

A $6 \mathrm{cm}$ side cube is cut into $1 \mathrm{cm}$ side cubes, then total surface area of all the small cubes will be:

Find the volume of the cubed whose respectively length breadth and height are $16.5 cm, 8.4 cm, 12.7 cm.$

The volume of a right circular cone which is obtained from a wooden cube of edge $4.2 \mathrm{dm}$ wasting minimum amount of wood is:

How many bricks, each of dimensions $25 \mathrm{cm}\times 16 \mathrm{cm}\times 10 \mathrm{cm}$ will be needed to build a wall $24 \mathrm{m} \mathit{\text{long}} 6 \mathrm{m}\text{ high and }0.4 \mathrm{m}\text{ thick. }$?

If the length of the side of a cube is tripled, show that its volume increases $27$ times. If the length of the side of a cube is halved, what is the change in its volume?

An open rectangular tank when measured from outside is $2.5 \mathrm{m}$ long, $2 \mathrm{m}$ broad and $60 \mathrm{m}$ deep and made of plastic which is $3.5 \mathrm{cm}$ thick. Find the capacity of the tank and the volume of the plastic used.

Nihal forms a cuboid of dimensions $4 \mathrm{cm}\times 3 \mathrm{cm}\times 2 \mathrm{cm}$, using cubes of dimension $1 \mathrm{cm}$ each. How many more such cubes are needed to form a big cube of side $4 \mathrm{cm}$?

A solid metallic block of volume $2$ cubic metres is melted and recast into a rectangular bar of length $32 \mathrm{m}$ having a square base. If the weight of the block is $160 \mathrm{kg}$ and the biggest cube is cut off from the bar then what is the weight of the cube is?

If the ratio of volumes of two cubes is $27:64$, then the ratio of their surface area is:

A cube of side $12 \mathrm{cm}$, is painted blue on all the faces and then cut into smaller cubes each of side $3 \mathrm{cm}$. The total number of smaller cubes having none of their faces painted blue will be

If side of each cube is $3 \text{cm}$. Then Volume of given figure is 

A metal cube is completely submerged in a cylindrical vessel containing water. The diameter of the vessel is $30cm,$ the level of water is raised by $1\frac{41}{99} cm$ . The length of the edge of the cube is:

A vessel in the shape of a cuboid is $30 \mathrm{cm}$ long and $25 \mathrm{cm}$ wide. What should be its height to hold $4.5 \mathrm{litres}$ of water?

How many cubes of edge $4 \mathrm{cm}$ can be cut out from the cuboid whose length, breadth and height are $20 \mathrm{cm}, 18 \mathrm{cm}$ and $16 \mathrm{cm}$ respectively?

A closed box is made up of wood which is $1 \mathrm{cm}$ thick. The outer dimensions of the box is $5 \mathrm{cm}\times 4 \mathrm{cm}\times 7 \mathrm{cm}$. Find the volume of wood used.

How many bricks will be required to build a wall of $8 \mathrm{m}$ long, $6 \mathrm{m}$ height and $22.5 \mathrm{cm}$ thick, if each brick measures $25 \mathrm{cm}$ by $11.25 \mathrm{cm}$ by $6 \mathrm{cm}$?

Find the number of bricks, each measuring $25\mathrm{cm}\times 12.5\mathrm{cm}\times 7.5\mathrm{cm}$ required to construct a wall $6\mathrm{m}$ long, $5\mathrm{m}$ high and $0.5\mathrm{m}$ thick, while the cement and sand mixture occupies $\frac{1}{20}$ of the volume of the wall.

A rectangular water reservoir is $10.8 \mathrm{m}$ by $3.75 \mathrm{m}$ at the base. Water flows into it at the rate of $18 \mathrm{m}$ per second through a pipe having the cross section $7.5 \mathrm{cm}\times 4.5 \mathrm{cm}$. Find the height to which the water will rise in the reservoir in $30 \mathrm{minutes}$. [Write the answer in $\mathrm{m}$]

A rectangular reservoir is $120 \mathrm{m}$ long and $75 \mathrm{m}$ wide. At what speed per hour must water flow into it through a square pipe of $20 \mathrm{cm}$ wide so that the water rises by $2.4 \mathrm{m}$ in $18 \mathrm{hours}.$ [Write the answer in $\mathrm{km}/\mathrm{hour}]$

Water flows in a tank $150 \mathrm{m}\times 100 \mathrm{m}$ at the base, through a pipe whose cross-section is $2 \mathrm{dm}$ by $1.5 \mathrm{dm}$ at the speed of $15 \mathrm{km} \mathrm{per} \mathrm{hour}$. In what time, will the water be $3 \mathrm{metres}$ deep? [Write the answer in hours]