Surface Area of a Cube

Find the volume and surface area of a cube whose edge is $5 \mathrm{cm}$.

If the base area of vessel which is in the form of a cuboid is $A {\mathrm{cm}}^2$, the internal height of it is $25 \mathrm{cm}$ and the capacity is $1\frac{3}{4} \mathrm{litres}$, then find the value of $A$.

$50$ men took a dip in a water tank $40 \mathrm{m}$ long and $20 \mathrm{m}$ broad on a religious day. If the average displacement of water by a man is $4 {\mathrm{m}}^3$,  then the rise in the water level in the tank will be

If the volume of the cube is $512 {\mathrm{m}}^3$, then its surface area is $x {\mathrm{m}}^2$. Find $x$.

Each side of a cube is $3$ units. It is cut into cubes each of side $1$ unit. If the total surface area of all the smaller cube thus obtained is $k$ square units. Find the value of $k$

If the surface area of cube of side $8 \mathrm{cm}$ is $k {\mathrm{cm}}^2$, then find the value of $k$.

A village having a population of $3600$, requires $125$ litres of water per head per day. It has a tank $25\mathrm{m}$ long, $18\mathrm{}\mathrm{m}$ broad and $5\mathrm{}\mathrm{m}$ high. For how many days the water of the tank will last?

The outer dimensions of a closed wooden box are $12\mathrm{}\mathrm{c}\mathrm{m}$ by $10\mathrm{}\mathrm{c}\mathrm{m}$ by $9\mathrm{}\mathrm{c}\mathrm{m}$. Thickness of wood is $1.5\mathrm{c}\mathrm{m}$. Find the total cost of wood required to make the box, if $1{\mathrm{c}\mathrm{m}}^3$ of wood costs $₹3.00$.

A rectangular water tank has $16200$ litres of water. The floor of the water tank is $4.5\mathrm{}\mathrm{m}\times 3\mathrm{}\mathrm{m}$. Find the height of water in the tank.

A cuboidal block of metal measuring $45\mathrm{}\mathrm{c}\mathrm{m}\times 30\mathrm{}\mathrm{c}\mathrm{m}\times 0.5\mathrm{}\mathrm{m}$ was melted and recast into cubical blocks each with an edge of length $3\mathrm{}\mathrm{c}\mathrm{m}$.
What is the cost of polishing the surfaces of the cubes at the rate of $₹1.25\mathrm{}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{}{\mathrm{c}\mathrm{m}}^2$?

The floor of a rectangular hall has a perimeter of $280\mathrm{}\mathrm{m}$, its height is $6\mathrm{}\mathrm{m}$. Find the cost of white washing the four walls (including door, windows etc.) at the rate of $₹10\mathrm{}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{}{\mathrm{m}}^2$.

The area of the four walls of a room is $156\mathrm{}{\mathrm{m}}^2$. The breadth and height of the room are $8\mathrm{}\mathrm{m}$ and $6\mathrm{}\mathrm{m}$ respectively. Find the length of the room.

A cubical cistern can contains $729$ litres. The area of its base is $k {\mathrm{dm}}^2$. Write the value of $k$

The volume of a cube is $1728 {\mathrm{m}}^3$. If its surface area is $k {\mathrm{m}}^2$, find the value of $k$.

Find the volume and surface area of a cube whose edge measures:
$1\frac{1}{2} \mathrm{m}$

Find the volume and surface area of a cuboid whose dimensions are:
$\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}=12.5 \mathrm{m},\mathrm{b}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{t}\mathrm{h}=5 \mathrm{m},\mathrm{h}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}=240 \mathrm{c}\mathrm{m}$

A cuboidal water tank contains $216$ litres of water. Its depth is $\frac{1}{3}$ of its length and breadth is $\frac{1}{2}$ of $\frac{1}{3}$ of the difference between length and depth. The length of the tank is: