A solid sphere is cut into two hemispheres. From one,a square pyramid and from the other a cone, each of maximum possible size are carved out. What is the ratio of their volumes?

What is the volume of the cone of maximum size that can be carved from a cube of edge 12 centimetres?

What is the base edge of a square pyramid of maximum size that can be carved out from a hemisphere of radius 5 cm?

A solid sphere of radius 12 centimetres is cut into two equal halves. What is the surface area of each hemisphere?

Three solids a square pyramid,a cone anda sphere have been carved out from three solid cubes of the same size. Find the volume of each solid.

The radius of a solid sphere is 6 centimetres. Find its volume and surface area.It is cut into two equal halves. What is the total surface area of each hemisphere? What is the volume of a hemisphere?

A rope of length 40 metres is cut into two pieces and two squares are made on the floor with them. The sum of the. area enclosed is 58 square meter. a) If the length of one piecce is taken as 'x', what is the. length of the other piece. b) What are the lengths of the sides of the squares? c) Write the. given fact about area as an algebraic equation. d) What is the length of each piece?

There are 30 scouts and 20 guides in a school In another school, there are 20 scouts and 15 guides From each school, one student among them is to be selected for participation in a seminar a) What is the total number of possible selections? b) What is the probability of both being Scouts? c) What is the probability of both being guides? d) What is the probability of one scout and one guide?

A piece of wood in the shape of a square prism has each side of the base 4 cm Iong and its height is 50 cm . What is the maximum volume of a cylinder that can be carved from it?

A wire of length 28 m is cut into two pieces. One of the Pieces is be made into a square and the other in to a circle. What should be the length of the two pieces so that combined area of the square and the circle is minimum using differentiation?