面積與體積

In the figure, $ABCD$ is a square of side $10\text{ cm}$. If $AE=AF$ and the area of $\triangle CEF$ is $20\text{ cm}^2$, which of the following equations can be used to find $AF$?

In the figure, the radii of the two circles are $3\text{ cm}$ and $1\text{ cm}$ respectively. Find the ratio of the area of the shaded part to that of the smaller circle.

The figure shows a right circular cone of base radius $4\text{ cm}$ and height $3\text{ cm}$. Find the area of its curved surface.

In the figure, find the area of the pentagon $ABCDE$.

The figure shows a test tube consisting of a cylindrical upper part of radius $1\text{ cm}$ and a hemispherical lower part of the same radius. If the height of the test tube is $12\text{ cm}$, find its capacity.

In the figure, $OABC$ is a sector. Find the area of the shaded region.

In the figure, a right pyramid with a square base is divided into three parts $A$, $B$ and $C$ by two planes parallel to the base such that the lengths of their slant edges are $1\text{ cm}$, $2\text{ cm}$ and $3\text{ cm}$ respectively. Find volume of $A$ : volume of $B$ : volume of $C$.

In the figure, $ABC$ is a semicircle. Find the area of the shaded part.

In the figure, $BEA$ is a semicircle. $ABCD$ is a rectangle and $DC$ touches the semicircle at $E$. Find the area of the shaded region.

In the figure, $BCA$ is a semicircle. If $AC=6$ and $CB=4$, find the area of the semicircle.