A juice seller was serving his customers using glasses as shown in the figure. The inner diameter of the cylindrical glass was $5 \mathrm{cm}$, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was $10 \mathrm{cm}$, find the apparent capacity of the glass and its actual capacity. (Use $\mathrm{\pi }=3.14$.)

 

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $2 \mathrm{cm}$ and the diameter of the base is $4 \mathrm{cm}$. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. (Take $\mathrm{\pi }=3.14$)

The radii of the ends of a frustum of a cone $45 \mathrm{cm}$ high are $28 \mathrm{cm}$ and $7 \mathrm{cm}$. Find its volume, the curved surface area and the total surface area (Take $\mathrm{\pi }=\frac{22}{7}$).

Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as $30 \mathrm{cm}$ and $35 \mathrm{cm}$ and the vertical height of the mould is $14 \mathrm{cm}$. If each ${\mathrm{cm}}^3$ of molasses has mass about $1.2 \mathrm{g}$, find the mass of the molasses that can be poured into each mould.$\left(\mathrm{Take} \mathrm{\pi }=\frac{22}{7}\right)$

An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The diameters of the two circular ends of the bucket are $45 \mathrm{cm}$ and $25 \mathrm{cm}$, the total vertical height of the bucket is $40 \mathrm{cm}$ and that of the cylindrical base is $6 \mathrm{cm}$. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold Take $\mathrm{\pi }=\frac{22}{7}$. 

The marks obtained by $30$ students of Class $X$ of a certain school in Mathematics paper consisting of $100$ marks are presented in the table below. Find the mean of the marks obtained by the students.

The table below gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers by all three methods.