The total surface area of a hemisphere is $41.58 \text{ cm}^2$. Find its curved surface area (in $\text{cm}^2$).

The respective ratio of the curved surface area and total surface area of a cylinder is $4:5$. If the curved surface area of the cylinder is $1232 \, cm^2$,what is the height? (in $cm$)

How many small cubical blocks of side $5\, cm$ can be cut from a cubical block whose each edge measures $20\, cm$?

If each edge of a cube is increased by $50 \%$,the percentage increase in surface area is (in $\%$)

The sum of the radius of the base and the height of a solid cylinder is $37 \, m$. If the total surface area of the cylinder is $1628 \, m^2$,find the volume (in $m^3$).

The base of a right pyramid is an equilateral triangle of side $4 \text{ cm}$. The height of the pyramid is half of its slant height. Its volume is ........ $\text{cm}^3$.