面積與體積

The figure shows a solid platform with steps on one side and a slope on the other. Find its volume.

In the figure, $TP$ and $TQ$ are tangents to the circle of radius $3\text{ cm}$. Find the length of the minor arc $PQ$.

Find the ratio of the volume of the tetrahedron $ACHD$ to the volume of the cube $ABCDEFGH$ in the figure.

In the figure, the equilateral triangle $ACE$ of side $4\text{ cm}$ is inscribed in the circle. Find the area of the inscribed regular hexagon $ABCDEF$.

In the figure, a cone of height $3h$ is cut by a plane parallel to its base into a smaller cone of height $h$ and a frustum. Find the ratio of the volume of the smaller cone to the volume of the frustum.

In the figure, $ABCD$ is a square of side $a$ and $MNPQ$ is a square of side $b$. The four trapeziums are identical. The area of the shaded region is

An equilateral triangle and a square have equal perimeters. $\dfrac{\text{Area of the triangle}}{\text{Area of the square}}=$

In the figure, $XPY$ and $YQZ$ are semi-circles with areas $A_1$ and $A_2$ respectively. $\angle YXZ=60^\circ$ and $\angle YZX=45^\circ$. The ratio $A_1:A_2=$

From a rectangular metal sheet of width $3\text{ cm}$ and length $40\text{ cm}$, at most how many circles each of radius $1\text{ cm}$ can be cut?

In the figure, the circular cylinder and the circular cone have the same height. The radius of the base of the cylinder is twice that of the cone. If the volume of the cone is $20\text{ cm}^3$, what is the volume of the cylinder?