From a solid sphere of radius $R$, a concentric solid sphere of radius $\dfrac{R}{2}$ is removed. The total surface area increases by

The volume of triangular prism whose adjacent sides are $\bar a,\ \bar b,\ \bar c$ each of magnitude $4$ units and each is inclined at an angel $\dfrac {\pi}{3}$ with other two is  

If angle of minimum deviation through an equilateral prism is $40^o$, angle of incidence (being equal to angle of emergence) would be

If a regular square pyramid has a base of side $8 cm$ and height of $30 cm$, then its volume is

A square pyramid can contain $16\ m^3$ of water. The height of the pyramid is $3\ m$. Calculate the length of base of the square pyramid.

$VPQRS$ is rectangle based pyramid where $PQ = 30\ cm, QR = 20\ cm$ and volume is $2000\ {cm}^3$, then height (in cm) is

State whether true or false : 

The base of right prism is a triangle whose perimeter is 28 cm and the inradius of the triangle is 4 cm. If the volume of the prism is 366 cc, then its height is 

For a prism, $A = 60^o$, $\mu = \sqrt{\dfrac{7}{3}}$, then the minimum possible angle of incidence, so that the light ray is refracted from the second surface is

The slant height of a right pyramid having square base of side $10cm$ and vertical height $15cm$ is

Consider an incomplete pyramid of balls on a square base having $18$ players, and having $13$ balls on each side of the top layer. Then the total number $N$ of balls in that pyramid satisfies 

The circumference of a 1 cm thick pipe is 44 cm. The level of water that 7 cm of pipe can hold is

The base of a right prism is a square of perimeter 20 cm and its height is 30 cm. The volume of the prism is

The base of a right prism is an equilateral triangle of edge $12$m. If the volume of the prism is $288\sqrt 3m^3$, then its height is: