面積與體積

In the figure, the paper cup in the form of a circular cone contains $10\text{ ml}$ of water. How many ml of water must be added to fill up the paper cup?

In the figure, $ABCD$ is a rectangular field of length $p$ metres and width $q$ metres. The path around the field is of width $2$ metres. Find the area of the path.

In the figure, $OACB$ is a sector of radius $r$. If $\angle AOB=\dfrac{\pi}{3}$, find the area of the shaded part.

Find the perimeter of the sector in the figure.

In the figure, the base of the conical vessel is inscribed in the bottom of the cubical box. If the box and the conical vessel have the same capacity, find $h:r$.

The figure shows a solid consisting of a cylinder of height $h$ and a hemisphere of radius $r$. The area of the curved surface of the cylinder is twice that of the hemisphere. Find the ratio volume of cylinder : volume of hemisphere.

In the figure, the rectangle has perimeter $16\text{ cm}$ and area $15\text{ cm}^2$. Find the length of its diagonal $AC$.

In the figure, $ABCD$ is a square and $ABE$ is an equilateral triangle. $\dfrac{\text{Area of }ABE}{\text{Area of }ABCD}=$

In the figure, the radii of the sectors $OPQ$ and $ORS$ are $5\text{ cm}$ and $3\text{ cm}$ respectively. $\dfrac{\text{Area of shaded region}}{\text{Area of sector }OPQ}=$

In the figure, $ABC$ is an equilateral triangle and the radii of the three circles are each equal to $1$. Find the perimeter of the triangle.