Surface area of a cube is $600\, cm^{2}$. Find out the length of its diagonal.

The height of a cylinder is decreased by $8 \%$,keeping its radius unchanged. What is the percentage change in its volume?

$A$ roller is $120 \, cm$ long and has a diameter of $84 \, cm$. If it takes $500$ complete revolutions to level a playground,determine the cost of levelling at the rate of $30 \, \text{paise}$ per $m^2$ (in $Rs.$). (Use $\pi = \frac{22}{7}$)

The base of a $10\, cm$ high solid cylinder is a semi-circle of radius $7\, cm$. Its total surface area (in $cm^2$) is (Use $\pi = \frac{22}{7}$)

The length of an edge of a hollow cube opened at one face is $\sqrt{3}$ metres. What is the length of the largest pole that it can accommodate?

$A$ solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal,then the ratio of the radius and height of its conical part is