面積與體積

A solid metal sphere of volume $252\text{ cm}^3$ is melted and recast into 3 smaller solid spheres whose radii are in the ratio $1:2:3$. The volume of the smallest sphere is

The base radii of two right circular cylinders are in the ratio $2:3$. If the two cylinders have the same height, what is the ratio of their curved surface area?

In the figure, the radius of the sector is $r$ and $\angle PAQ=x^\circ$. If the area of the sector is $A$, then $x=$

In the figure, all the corners are right-angled. If the perimeter of the figure is $40$, then $x=$

If the lengths of the diagonals of a rhombus are $2\text{ cm}$ and $4\text{ cm}$ respectively, what is the area of the rhombus?

A hollow cylindrical metal pipe, $1\text{ m}$ long, has an external radius and an internal radius of $5\text{ cm}$ and $4\text{ cm}$ respectively. The volume of metal is

In the figure, $OAB$ is a sector of a circle. Radius $OA$ is $3\text{ cm}$ long and arc $AB=2\text{ cm}$. The area of the sector is

A solid sphere is cut into two hemispheres. The percentage increase in the total surface area is

A right circular cone of altitude $3r$ and base radius $r$ has the same volume as a cube of side $x$. $x=$

Some air escapes from a spherical balloon of volume $a^3$. The balloon keeps its spherical shape and is now of volume $b^3$. What is the percentage decrease in the radius?