面積與體積

In the figure, $OXY$ is a sector with centre $O$. If $Z$ is the mid-point of $YO$, find area of $\triangle OXZ$ : area of sector $OXY$.

In the figure, the rocket model consists of three parts. Parts I and III can be joined together to form a right circular cone. Part II is a right cylinder. Find the volume of the rocket model.

In the figure, $O$ is the centre of the circle. $AB$ and $AC$ are tangents to the circle at $B$ and $C$ respectively. Area of the shaded region $=$

In the figure, the area of $ABCD$ is

In the figure, A and B are two right solid cylinders with the same base radius $1$. If the heights of A and B are $1$ and $2$ respectively, find $\dfrac{\text{the total surface area of A}}{\text{the total surface area of B}}$.

The figure shows a frustum of a right circular cone. The radii of the upper face and the base are $1\text{ cm}$ and $2\text{ cm}$ respectively. If the height is $3\text{ cm}$, find the volume.

In the figure, $ABCD$ is a trapezium. Find its area.

In the figure, the solid consists of a cylinder and a right circular cone with a common base which is a circle of radius $3\text{ cm}$. The height of the cylinder is $10\text{ cm}$ and the slant height of the cone is $5\text{ cm}$. Find the total surface area of the solid.

In the figure, $O$ is the centre of the circle. Find the area of the major segment $ABC$.

In the figure, $C_1$ and $C_2$ are two circles. If area of region I : area of region II : area of region III $=2:1:3$, then radius of $C_1$ : radius of $C_2=$