$A$ solid consisting of a right circular cone of height $120\, cm$ and radius $60\, cm$ standing on a hemisphere of radius $60\, cm$ is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder,if the radius of the cylinder is $60\, cm$ and its height is $180\, cm$. [Take $\pi = \frac{22}{7}$.] (in $m^3$)

$A$ medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). The length of the entire capsule is $14 \, mm$ and the diameter of the capsule is $5 \, mm$. Find its surface area. $\left[ \text{Use } \pi = \frac{22}{7} \right]$ (in $mm^2$)

How many silver coins,$1.75 \,cm$ in diameter and of thickness $2 \,mm$,must be melted to form a cuboid of dimensions $5.5 \,cm \times 10 \,cm \times 3.5 \,cm$? [Take $\pi = \frac{22}{7}$]

$A$ wooden article was made by scooping out a hemisphere from each end of a solid cylinder,as shown in the figure. If the height of the cylinder is $10 \, cm$ and its base radius is $3.5 \, cm$,find the total surface area of the article (in $cm^2$).

$A$ 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 $26\, cm,$ while the height of the conical part is $6\, cm.$ The base of the conical portion has a diameter of $5\, cm,$ while the base diameter of the cylindrical portion is $3\, cm.$ 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. (in $cm^2$) (Take $\pi=3.14$)

$A$ metallic sphere of radius $4.2 \, cm$ is melted and recast into the shape of a cylinder of radius $6 \, cm$. Find the height of the cylinder. (in $cm$) [Take $\pi = \frac{22}{7}$]