The radius of a cylinder is made twice as large. How should the height be changed so that its volume remains unchanged?

The base of a right prism is an equilateral triangle. If the lateral surface area and volume are $120 \, cm^2$ and $40 \sqrt{3} \, cm^3$,respectively,then the side of the base of the prism is ...... $cm$.

The volume of a right circular cone is $1232\, cm^3$ and its vertical height is $24\, cm$. Its curved surface area is.......$cm^2$.

$A$ solid cylinder having a radius of base as $7 \, cm$ and length as $20 \, cm$ is bisected along its height to get two identical cylinders. What will be the percentage increase in the total surface area?

The length of the diagonal of a cube is $6 \text{ cm}$. The volume of the cube (in $\text{cm}^3$) is (in $\sqrt{3}$)

$A$ cylindrical can with a horizontal base and an internal radius of $3.5 \, cm$ contains sufficient water so that when a solid sphere is placed inside,the water just covers the sphere. The sphere fits exactly into the can. The depth of the water in the can before the sphere was added is: