The decorative block shown in the figure is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge $5 \, cm$,and the hemisphere fixed on the top has a diameter of $4.2 \, cm$. Find the total surface area of the block. (in $cm^2$) (Take $\pi = \frac{22}{7}$)

Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder (see figure). If the base of the shed is of dimension $7\,m \times 15\,m,$ and the height of the cuboidal portion is $8\,m,$ find the volume of air that the shed can hold. Further,suppose the machinery in the shed occupies a total space of $300\,m^3,$ and there are $20$ workers,each of whom occupy about $0.08\,m^3$ space on an average. Then,how much air is in the shed? (in $m^3$) (Take $\pi = \frac{22}{7}$)

$A$ farmer connects a pipe of internal diameter $20 \,cm$ from a canal into a cylindrical tank in her field,which is $10 \,m$ in diameter and $2 \,m$ deep. If water flows through the pipe at the rate of $3 \,km/h$,in how much time will the tank be filled? (in $minutes$) [Take $\pi = \frac{22}{7}$]

$A$ juice seller was serving his customers using glasses as shown in the figure. The inner diameter of the cylindrical glass was $5 \, cm$,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 $10 \, cm$,find the apparent capacity of the glass and its actual capacity (in $cm^3$). (Use $\pi = 3.14$)

In one fortnight of a given month,there was a rainfall of $10 \, cm$ in a river valley. If the area of the valley is $7280 \, km^2$,show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each $1072 \, km$ long,$75 \, m$ wide,and $3 \, m$ deep.

$A$ fez,the cap used by the Turks,is shaped like the frustum of a cone (see $Fig.$). If its radius on the open side is $10 \, cm$,radius at the upper base is $4 \, cm$ and its slant height is $15 \, cm$,find the area of material used for making it.