Question 1 : Radius and slant height of a solid right circular cone are in the ratio $3:5$. If the curved surface area is $60\pi sq.cm$, then find its total surface area.

Question 2 : A cylinder and a cone have the same height and same radius of the base. The ratio of the volumes of the cylinder to that of the cone is ________.

Question 3 : The radius of a sphere is 3 cm its volume is

Question 4 : A cylindrical rod of iron whose height is four times its radius is melted and cast into the spherical balls of the same radius then the number of balls is

Question 5 : A right circular cone and a cylinder have a circle of unit radius as base and their heights are equal to the radius itself and a hemisphere has the same radius then their volumes are proportional respectively to

Question 6 : The ratio of the radii of two cones having equal height is $2:3$, then ratio of their volume is ____________.

Question 7 : If the circumference of the inner edge of a hemispherical bowl is $\dfrac {132}{7} cm$, then what is its capacity?

Question 8 : The volume of a solid hemisphere of radius 2 cm is

Question 9 : If the radius of the base of a right circular cone is $3r$ and its height is equal to the radius of the base, then its volume is:

Question 10 : If the radius height of a cone are in the ratio 5 : 12 and its volume is$ \displaystyle 314cm^{3} $ then slant height is

Question 11 : Two right circular cones of dimensions h=4.1, r=2.1 cm and h = 4.3 cm, r = 2.1 cm are melted to form a sphere of radius

Question 12 : A cone of semi-vertical angle $\displaystyle \alpha $ is inscribed in a sphere of radius $2$ cm. The height of the cone is 

Question 13 : The ratio of the volumes of two spheres is $8 : 27$. The ratio of their radii is<br/>

Question 14 : The diameter of two right circular cones are equal. If their slant heights are in the ratio $3 : 2$, then what is the ratio of their curved surface areas?

Question 16 : The volume of a sphere of diameter 2p cm is given by

Question 17 : The volume of the greatest sphere cut off from a cylindrical wood of base radius 1 cm and height 5 cm is

Question 18 : The radii of two right circular cone are in the ratio of 4 : 5 and their slant heights are in the ratio 2 ; 3. Then the ratio of their curved surfaces is

Question 19 : The volume of a sphere is $\dfrac {88}{21}\times (14)^{3} cm^{3}$. The curved surface of the sphere is (Take $\pi = \dfrac {22}{7}$).

Question 20 : How many spherical bullets can be made out of a cube of lead whose edge measures $22$cm, each bullet being $2$cm in diameter?

Question 21 : A conical cup has a circular base with diameter $21\;cm$ and height $1.8\;dm$. How much oil can it contain?

Question 22 : Find the volume of the right circular cone with&#160;radius $3.5\ cm$, height $12\ cm$

Question 23 : A conical cup $18$ cm high has a circular base of diameter $14$ cm The cup is full of water which is now poured into a cylindrical vessel of circular base whose diameter is $10$ cm What will be the height of water in the vessel

Question 24 : Two cones $A$ and $B$ have their base $r$ in the ratio of $4:3$ and their heights in the ratio $3:4$ of ratio of volume of cone $A$ to that of cone.

Question 25 : There is water to a height of $16cm$ in a cylindrical glass jar of radius $12.5cm$. Inside the water, there is a sphere of diameter $15cm$, completely immersed. By what height will water go down, when the sphere is removed?

Question 26 : The radius of a sphere of lead is $8$cm. The number of spheres of radius $5$mm made by melting it will be

Question 27 : The surface area of a sphere is$\displaystyle 5544cm^{2}$. Its volume is

Question 28 : If a sphere and a cube have the same volume then the ratio of the surface of the sphere to that of the cube is

Question 29 : A right triangle with sides 5 cm 12 cm and 13 cm is revolved about the side 12 cm Find the volume of the cone thus formed

Question 30 : The largest sphere is carved out of a cube of edge 14 cm Find the volume of the sphere

Question 31 : If the sum of the radii of two spheres is 2 km and their volumes are in the ratio 64:27 then the ratio of their radii is

Question 32 : The radius and height of a right circular cone are in th ratio $2:3$. Find the slant height if its volume is $100.48\ cm^3$. (Take $\pi =3.14$).

Question 33 : Find the volume and surface area of a sphere of radius $4.2$ cm. $\displaystyle \left [ \pi =\frac{22}{7} \right ]$<br/>

Question 35 : The volume of frustum of a cone is calculated by usingthe formula ______

Question 36 : The number of spherical bullets each $0.6$ cm in diameter be made out of a rectangular solid $9$ cm $\times$ $11$ cm $\times 12$ cm is __________.

Question 37 : Three spheres of radii 6 cm, 8 cm and 10 cm are melted to form a sphere of radius

Question 38 : The number of balls of radius $1$ cm that are made from a solid sphere of radius $4$ cm

Question 39 : A right circular cone an and circular and a right cylinder have the same radius and the same volume. The ratio of the height of the cone to that of the cylinder is

Question 40 : The volume of a hemispherical ball is given by the$\displaystyle V=\frac{2}{3}\pi r^{3}$ where V is the volume and r is the radius Find the diameter of he hemisphere whose volume is$\displaystyle \frac{468512}{21}m^{3}$

Question 41 : Find the slant height of a cone whose,<br>Base radius $=14\;cm$, height $0.48\;m$<br>Base diameter $=70\;cm$, curved surface area $=4070\;cm^2$

Question 43 : A cylindrical pencil sharpened at one edge is the combination of<br>

Question 44 : The height of a cone is $9 cm$ and the radius of the base is $7 cm$. The cone is melted and a cuboid is formed. The length of the base of the cuboid is $11 cm$ and breadth is $6 cm$. Find the height of the cuboid.<br>

Question 45 : A metallic hemisphere is melted and recast in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then.

Question 46 : The volume of a sphere is increasing at the rate of 1200c.cm/sec.The rate of increase in its surface area when the radius is 10 cm is.

Question 47 : How many metres of plastic sheet, $5\;m$ wide, will be required to make a conical tent, the radius of whose base is $7\;m$ and height is $24\;m$ ?

Question 48 : Three solid spheres of copper, whose radii are $3$ cm, $4$ cm and $5$ cm respestively are melted into a single solid sphere of radius R. The value of R is

Question 49 : If the base area and the volume of a cone are numerically equal, then its height is 3 units.<br>

Question 50 : Find the weight of a solid cone whose base is of diameter $42\;cm$ and vertical height $20\;cm$, supposing that the material of which it is made weights $5$ grams per cubic centimetre.