A solid wood piece is made up of two pieces joined at right angles. The face ABCDEFA is the uniform cross section. Assuming all the angles A,B,C,D,E and F to be right angles, find the volumes of the piece

An ellipse has O B as the semi-minor axis, Fa n dF ' as its foci, and /_F B F ' a right angle. Then, find the eccentricity of the ellipse.

A right angled triangle of which the sides containing the right angle are 6.3cm and 10cm in length, is made to turn around on the longer side. Find the volume of the solid thus generated.

In a right angle triangle ABC, let b = 10, c = 10 sqrt(2) find a.

A wire of uniform cross section has a resistance of 9 Omega. It is cut into three equal pieces. Each piece is stretched uniformly to three times its length and all the three stretched pieces are connected in parallel.Assuming that stretching of wire does not cause any change in density of their material ,calculate the total resistance of the combination described.

let ABC be a right angled triangle at C. If the inscribed circle touches the side AB at D and (AD) (BD)=11, then find the area of triangle ABC. .

The misture a pure liquid and a solution in a long vertical column (i.e., horizontal dimensions << vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. A ray of light entering the column at right angles to the vertical is deviated from its original path. find the deviation in travelling a horizontal distance d << h, the heigh of the column.

O is the origin and A is (a,b,c). Find the d.c. of OA and the equation of the plane through A at right angles of OA.

In triangle ABC, right angled at B, if tan A = 1/sqrt3 . Find the value of :- cos A cos C -sin A sin C.

Monica has a piece of canvas whose area is 551 m^2 . She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m^2 , find the volume of the tent that can be made with it.