面積與體積

In the figure, a solid wooden sphere of radius $r$ cm is to be cut into a cube of side $3\text{ cm}$. Find the smallest possible value of $r$.

In the figure, $ABCDEF$ is a right triangular prism. It is cut into two parts along the plane $PQRS$, which is parallel to the face $BCDF$, and $AP:PB=2:5$. Find $\dfrac{\text{volume of the prism }APQRES}{\text{volume of the prism }ABCDEF}$.

$\pi$ degrees $=$

In the figure, a square is inscribed in a circle with radius $1\text{ cm}$. Find the area of the shaded region.

The figure shows a right prism. Find its total surface area.

In the figure, a cylindrical vessel of internal diameter $6\text{ cm}$ contains some water. A steel ball of radius $2\text{ cm}$ is completely submerged in the water. Find the rise in the water level.

In the figure, the solid consists of a right circular cone and a hemisphere with a common base. Find the volume of the solid.

In the figure, $ABCD$ is a semicircle. Find the area of the shaded region correct to the nearest $0.01\text{ cm}^2$.

In the figure, a right circular cone is divided into two parts $X$ and $Y$ by a plane parallel to the base such that the lengths of their slant edges are $4\text{ cm}$ and $3\text{ cm}$ respectively. Find the ratio of the curved surface areas of $X$ and $Y$.

The figure shows five sectors. Which of the marked angles measures $2$ radians?