1999 年

In the figure, a square is inscribed in a circle with radius $1\text{ cm}$. Find the area of the shaded region.

The figure shows a right prism. Find its total surface area.

In the figure, a cylindrical vessel of internal diameter $6\text{ cm}$ contains some water. A steel ball of radius $2\text{ cm}$ is completely submerged in the water. Find the rise in the water level.

In the figure, the solid consists of a right circular cone and a hemisphere with a common base. Find the volume of the solid.

In the figure, $ABCD$ is a semicircle. Find the area of the shaded region correct to the nearest $0.01\text{ cm}^2$.

In the figure, $O$ is the centre of the circle. Find $x$.

In the figure, $AB$ is a diameter of the circle. Find $x$.

In the figure, $ACD$ and $ECB$ are straight lines. If $\angle EAC=\angle CAB$ and $EA=EB$, find $x$.

In the figure, $ABCDE$ is a regular pentagon and $ABFG$ is a square. Find $x$.

In the figure, $AEB$ and $ADC$ are straight lines. Find $ED$.