The base of a cone with radius $7\, cm$ and height $24\, cm$ is hemispherical. Find the cost of painting its surface at the rate of ₹ $2/cm^2$. (in ₹)

How many balls of radius $1.4 \, cm$ can be produced by melting a metallic sphere of radius $42 \, cm$?

The radius and height of a cone are $5\,cm$ and $12\,cm$ respectively. Then,the ratio of its $CSA$ and area of base is $\ldots \ldots \ldots \ldots$

$A$ factory manufactures $120000$ pencils daily. The pencils are cylindrical in shape,each of length $25 \,cm$ and circumference of base $1.5 \,cm$. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at $\operatorname{Rs.} 0.05$ per $dm^2$ (in $Rs.$).

$A$ cone is cut by a plane parallel to its base and the smaller cone formed on the upper side of the plane is removed. The remaining part on the other side of the plane is called:

Write 'True' or 'False' and justify your answer:
An open metallic bucket is in the shape of a frustum of a cone,mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.