面積與體積

The figure shows two sectors with radii $r$ and $2r$. If these two sectors are equal in area, then $\theta_1:\theta_2=$

In the figure, $ABCD$ is a straight line with $AB=BC=CD$. Three circles I, II and III are drawn respectively on $AB$, $AC$ and $AD$ as diameters. Areas of circle I : Area of circle II : Area of circle III $=$

In the figure, if the area of the sector is $x$, then arc $ACB=$

$ABCDEFGH$ is a cube of side $3\text{ cm}$. A tetrahedron $DACH$ is cut away along the plane $ACH$. The volume of the remaining solid is

The total surface area of a regular tetrahedron of side $3\text{ cm}$ is

In the figure, a regular hexagon of side $2\text{ cm}$ is inscribed in a circle. The area of the circle is greater than the area of the hexagon by

A cone of base radius $2r\text{ cm}$ and height $h\text{ cm}$ has a volume of $60\text{ cm}^3$. The volume of a cylinder of base radius $r\text{ cm}$ and height $4h\text{ cm}$ is

In the figure, the volumes of the pyramids $VABC$ and $VPQR$ are $27\text{ cm}^3$ and $64\text{ cm}^3$ respectively. Planes $ABC$ and $PQR$ are parallel. Area of $\triangle ABC$ : Area of $\triangle PQR=$

A rectangular box, without a lid, is 40 cm long, 30 cm wide and 10 cm high. The area of the external surface of the box is

The external and internal radii of a hollow metal sphere are 4 cm and 3 cm respectively. $\dfrac{\text{Volume of metal}}{\text{Volume of the enclosed empty space}}=$