An electrician has to repair an electric fault on a pole of height $5 \mathrm{m}$. She needs to reach a point $1.3 \mathrm{m}$ below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of $60°$ to the horizontal, would enable her to reach the required position? Also, how far from the foot of the pole should she place the foot of the ladder? (You may take $\sqrt{3}=1.73$)

Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is $5 \mathrm{cm}$ in height and the diameter of the top is $3.5 \mathrm{cm}$. Find the area he has to colour. (Take $\mathrm{\pi }=\frac{22}{7 }$).

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in the figure. The height of the entire rocket is $26 \mathrm{cm}$, while the height of the conical part is $6 \mathrm{cm}$. The base of the conical portion has a diameter of $5 \mathrm{cm}$, while the base diameter of the cylindrical portion is $3 \mathrm{cm}$. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take $\mathrm{\pi }=3.14$)

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

A juice seller was serving his customers using glasses as shown in the figure. The inner diameter of the cylindrical glass was $5 \mathrm{cm}$, 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 $\mathrm{\pi }=3.14$.)