Question 1 :
The volume of the hemisphere is$\displaystyle2100{ cm }^{ 3 }$. Find its radius.(Round off your answer to the nearest whole number).

Question 2 :
The diameter of a copper sphere is $6\ cm$. It is beaten and drawn into a wire of diameter $0.2\ cm$. The length of wire is ........

Question 3 :
The volume of a sphere is $38808\ cu.cm$. The curved surface area of the sphere (in ${cm}^{2}$) is:

Question 4 :
The internal and external radii of a hemispherical metallic vessel are $7\ cm$ and $10.5\ cm$ respectively. If $1\ cm^{3}$ of the metal weighs $10\ g$, find the weight of the vessel

Question 5 :
The curved surface of a circular cylinder of height $'h'$ and the curved surface area of the cone of slant height  $'2h'$ having the same circular base, are in the ratio of

Question 6 :
If a solid right circular cylinder&#160; made of iron is heated to&#160; increase its radius and height&#160; by $1 \%$. each, then the volume&#160; of the solid is increased by<br/>

Question 7 :
The internal length, breadth and height of a &#160;box are $30$ cm, $24$ cm and $15$ cm. Find the largest number of cubes that can be placed inside this box if the edge of each cube is $5$ cm.

Question 8 :
A cube with &#160;an edge length $4$ is divided into $8$ identical cubes. Calculate the difference between the combined surface area of the $8$ smaller cubes and the surface area of the original cube.

Question 9 :
A cylindrical&#160;container of radius $6\ &#160;cm$ and height $15 \ cm$ is filled with ice-cream. The whole&#160;ice cream has to be distributed to $10$ children in equal cones with hemispherical&#160;tops. The height of the conical portion is $4$ times the radius of its base, find&#160;the radius of the ice-cream cone.

Question 10 :
The internal and external radii of a metallic spherical shell are $4$ cm and $8$ cm, respectively. It is melted and recast into a solid right circular cylinder of height $9\displaystyle \frac{1}{3} $ cm. Find the diameter of the base of the cylinder.

Question 11 :
A cube with edges of length $b$ is divided into $8$ equal smaller cubes. Calculate the difference between the combined surface area of the $8$ smaller cubes and the surface area of the original cube.

Question 12 :
The number of solid spheres, each of diameter $6$cm that could be moulded to form a solid metal cylinder of height $45$cm and diameter $4$cm, is _______.

Question 13 :
Water is supplied to a city population for general use (not for drinking) from a river through a cylindrical pipe. The radius of the cross-section of the pipe is $20cm$. The speed of water through the pipe os $18km$ per hour. Find the quantity of water in litres which is supplied to the city in two hours. (Take $\pi=3.14$ and $1{m}^{3}=1000$litres)

Question 14 :
The volume of two cylinders are in the ratio $a : b$ and their heights are in ratio $c : d$. Find the ratio of their diameters.

Question 15 :
A cylindrical tank is $\dfrac{1}{2}$ full. When 6 quarts are added, the tank is $\dfrac{2}{3}$ full. The capacity of the tank, in&#160;quarts, is