Find out the cost of the log of wood measuring $15 \frac{1}{2} \text{ m}$ by $2 \frac{3}{4} \text{ m}$ by $1 \frac{1}{3} \text{ m}$ at ₹ $45$ per $\text{cm}^3$ (in ₹).

$A$ sphere is melted to form a cylinder whose height is $4 \frac{1}{2}$ times its radius. What is the ratio of the radius of the sphere to the radius of the cylinder?

$A$ school room is to be built to accommodate $70$ children,so as to allow $2.2\, m^2$ of floor area and $11\, m^3$ of space for each child. If the room is $14\, m$ long,what must be its breadth and height?

$A$ cylindrical bucket is $72\, cm$ high and $28\, cm$ in diameter and is full of water. This water is emptied into a rectangular tank whose length and breadth are $66\, cm$ and $28\, cm$,respectively. What will be the height of the water level in the tank? (in $cm$)

$3$ spherical balls of radii $1\, cm$,$2\, cm$,and $3\, cm$ are melted to form a single spherical ball. In the process,the loss of material is $25\%$. The radius of the new ball is.........$cm$.

The radius of a wheel is $3.5 \, cm$. What is the distance (in $cm$) travelled by the wheel in $20$ revolutions?