Question 1 :
Identify the volume of largest cone which can be carved out from a cube of edge '$a$' cm.

Question 2 :
The shape formed by rotating a right triangle about its height is

Question 3 :
Find the volume of a frustum cone, whose baseand upper area of a circle is 6 and 6$cm^2$. The height of thecone is 100 cm.

Question 4 :
A sphere and cube have equal surface areas. The ratio of their volumes is

Question 5 :
A right circular cylinder and a right circular cone both having the same radius and height then the ratio of their volumes is

Question 6 :
Diameter of the base of a cone is $10.5cm$ and its slant height is $10cm$. Find its curved surface area.

Question 7 :
A table lamp is in the shape of the frustum of a right circular cone whose curved area is $1200 m^2$ and the area of the base and top is $2400 m^2$. Find the total surface area of the frustum cone.<br/>

Question 8 :
Find the total surface area of a cone, if its slant height is $21m$ and diameter of its base is $24m$.

Question 9 :
<p>A vessel is inthe form of a frustum of a cone. Its radius at top end is 12 m and the bottomend is 10 m. Its volume is 369 $ \pim^3$. Findits height.</p>

Question 10 :
A sphere of radius $r$ lies inside a cube and touches each of the six sides of the cube. Calculate the volume of the cube in terms of $r$.

Question 11 :
Solid cylinders of equal volume are tightly packed in two layers in a rectangular box such that in each layer there are three rows of four such cylinders Find the percentage of volume of empty space in the box approximately.

Question 12 :
A drum is in the shape of a frustum of a cone. Its top and bottom radii are $20$ ft and $10$ ft respectively. Its height is $15$ ft. It is fully filled with water. This water is emptied into a rectangular tank. The base of the tank has the dimensions $100$ ft $\times 50$ ft. Find the rise in the height of the water level in the tank.