A cubical block of side 7cm is surmounted by a hemisphere.What is the greatest diameter of the hemisphere can have? Find the surface area of the solid.

A tent is in the shape of a cylinder surmounted by a conical top.If the height and diameter of the cylindrical part are 2.1m and 4m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent.Also, find the cost of the canvas of the tent at the rate of Rs.500 per m². [Note that the base of the tent will not be covered with canvas.]

From a solid cylindrical whose height is 2.4cm and diameter 1.4cm, a conical cavity of the same height and same diameter is hollowed out.Find the total surface area of the remaining solid to the nearest cm² .

Rachel, an engineering student, was asked make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet.The diameter of the model is 3cm and its length is 12cm.
If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made.(Assume the outer and inner dimensions of the model to be nearly the same.)

The sum of the radius of the base and the height of a solid cylinder is 37cm.If the total surface area of the of the solid cylinder is 1628cm², find the volume of the cylinder.\([\pi=22/7]\)

The length of a hall 20m and width 16m.The sum of the areas of the floor and the flat roof is equal to the sum of the four walls.Find the height and the volume of the hall.

A factory manufactures 1,20,000 pencils daily. The pencils are cylindrical in shape, each of length 25 cm and circumference 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at Rs. 0.05 per dm² .

A cone of height 10 cm and radius 10 cm is to be divided into two parts by cutting through the mid point of the vertical axis. Find the volume of the upper conical part.

The area of the base of a cone is 770 cm² and the curved surface area is 814 cm² . Find the volume of the cone.

One iron solid is a cuboid of dimensions 30cm x 30cm x 42.65cm.It is melted and cubes each of side 3cm are moulded from it.Find the number of cubes formed.

A plot of land in the form of a rectangle has dimensions 240 m x 180 m. A drainlet 10 m wide is dug all around it (on the outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. Find the depth of the drainlet.

A metallic right circular cone 20 cm high and whose vertical angle is 60^o is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter \(\frac{1}{16}\) cm, find the length of the wire.

Three cubes of metal whose edges are 3 cm, 4 cm and 5 cm are melted and a single cube is formed. Find the edge of the single cube so formed.

A circus tent is cylindrical upto a height of 3 m and conical above it. If the diameter of the base is 105 m and the slant height of the conical part is 53 m, find the total canvas used in making the tent.

An ice-cream cone consisting of a cone surmounted by a hemisphere. The radius of the hemisphere is 3.5 cm and height of the ice-cream cone is 12. 5 cm. Calculate the volume of the ice-cream in the cone.