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?

Find the length of the canvas $2 \ m$ in width required to make a conical tent $12 \ m$ in diameter and $6.3 \ m$ in slant height (in $m$).

Water flows into a tank with a base of $150\, m \times 100\, m$ through a pipe with a cross-section of $2\, dm \times 1.5\, dm$ at a speed of $15\, km/h$. In what time will the water reach a depth of $3\, m$? (in $hours$)

$A$ tent is in the shape of a right circular cylinder up to a height of $3\, m$ and then becomes a right circular cone with a maximum height of $13.5\, m$ above the ground. If the radius of the base is $14\, m$,find the cost of painting the inner side of the tent at the rate of ₹ $2$ per $m^2$ (in ₹).

$A$ 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

The curved surface area of a right circular cone of height $15\, cm$ and base diameter $16\, cm$ is..........$\pi\, cm^2$.