1984 年

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?

The greatest value of $\dfrac{3}{4+2\cos\theta}$ is

If $0^\circ\le\theta<360^\circ$, the number of roots of the equation $2\sin\theta+\dfrac{1}{\sin\theta}=3$ is

In the figure, $\angle B=90^\circ$ and $BCD$ is a straight line. If $AB=p$ and $BC=q$, then $\cos\theta=$

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, $PQRS$ is a square inscribed in $\triangle ABC$. $AB=AC$ and $PQ=a$. $AB=$

In the figure, $AB\parallel DC$. $AB=q$ and $DC=p$. $BC=$

In the figure, $XY\parallel BC$. $AX:XB=2:1$. If the area of the trapezium $BCYX=20$, then the area of $\triangle ABC=$

The figure shows the graph of $y=a\sin k\theta$. What are the values of the constants $a$ and $k$?