面積與體積

In a circle, the angle of a sector is $30^\circ$ and the radius is $2\text{ cm}$. The area of the sector is

In the figure, $OACB$ is a sector of a circle of radius $6\text{ cm}$. Arc $ACB$ is longer than the chord $AB$ by

In the figure an equilateral triangle is inscribed in a circle of radius $a$. What is the area of the triangle?

Four identical trapeziums, each of area $16\text{ cm}^2$, are drawn inside a square of side $10\text{ cm}$ as shown in the figure. What is the height of each trapezium?

The perimeter of the given figure $ABCDE$ is $2(\pi+4)\text{ cm}$. The upper portion $AED$ is a semi-circle and the lower portion $ABCD$ is a rectangle. $AB:BC=1:2$. What is the area of the given figure?

If the surface area of a spherical soap bubble increases by $44\%$, its volume increases by

The total area of the six faces of the solid cube in the figure is $96\text{ cm}^2$. What is the length of the diagonal $AB$?

In the figure, $ABCD$ is a quadrilateral. The shaded portions are four sectors with centres at $A$, $B$, $C$ and $D$. Their radii are all equal to $a$. What is the total area of the four sectors?

In the figure, $\angle BAC=90^\circ$, $AB=8$, $AC=5$ and $AX\perp BC$. $BCDE$ is a rectangle with $CD=AX$. What is the area of the rectangle $BCDE$?

The height of the cone in the figure is $h$. It contains water to a depth of $\dfrac{1}{2}h$. $\dfrac{\text{Volume of water}}{\text{Capacity of the cone}}=$