The diagonal of a cube is $8\sqrt{3} \mathrm{cm}$. If is volume is $V {\mathrm{cm}}^3$, then find the value of $V$.

A wooden cube made of plywood with edge $3 \mathrm{m}$ was painted all round at $₹ 58 \mathrm{per} {\mathrm{m}}^2$ for advertisement in a circus. Find the cost of painting.

The four walls and the roof of a rectangular hall were painted at $\mathrm{Rs} 16$ per ${\mathrm{m}}^2$ The length, breadth and height of the hall were $12 \mathrm{m}, 8 \mathrm{m}$ and $6 \mathrm{m}$ respectively. There were $6$ doors measuring $3 \mathrm{m}$ by $1 \mathrm{m}$ and $6$ windows measuring $1\frac{1}{2} \mathrm{m}$ by $1 \mathrm{m}$. Find the cost of painting.

A cuboid metal bar measuring $24 \mathrm{cm}$ by $16 \mathrm{cm}$ by $8 \mathrm{cm}$ was melted and recast into metal cubes of side $4 \mathrm{cm}$. If $x$ number of cubes were made if there was no loss of metal in the process, then find the value of $x$.

Six wooden cubes of edge $4 \mathrm{cm}$ were placed in a row to form a cuboid. If the total surface exposed is $k {\mathrm{cm}}^2$, find the value of $k$

A cardboard box measuring $24 \mathrm{cm}$ by $18 \mathrm{cm}$ by $12 \mathrm{cm}$ was made. It was closed at the bottom and open at the top. If the area of cardboard used is $k {\mathrm{cm}}^2$, find the value of $k$

A cardboard box measuring $24 \mathrm{cm}$ by $18 \mathrm{cm}$ by $12 \mathrm{cm}$ was made. It was closed at the bottom and open at the top. Calculate area of cardboard used. Calculate length of the longest rod that can be placed completely inside the box.

The diagonal of a cuboid is $\sqrt{1125} \mathrm{cm}$. Given that the length and breadth are $25 \mathrm{cm}$ and $20 \mathrm{cm}$ respectively, find height.

The diagonal of a cuboid is $\sqrt{1125} \mathrm{cm}$. Given that the length and breadth are $25 \mathrm{cm}$ and $20 \mathrm{cm}$ respectively, find total surface.