Q41 A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 3 cm, and the diameter of the base is 8 cm. If a right circular cylinder circumscribes the toy, find the difference between the volumes of the cylinder and the toy.

Q42 The sum of the radius of base and height of a solid right circular cylinder is 40 cm. If the total surface area of the solid cylinder is 1256sq. cm, find the volume of the cylinder.

Q43 A cylindrical vessel of diameter 10cm and height 25cm is fixed symmetrically inside a similar vessel of diameter 30cm and height 25cm. The total space between two vessels is filed with cork dust for heat insulation purposes. How many cubic cms of cork dust will be required?

Q44 From a sheet of cardboard in the shape of a square of side 15cm, a piece in the shape of letter B is cut off. The curved side of the letter consists of two equal semicircles and breadth of the rectangular piece is 2cm. Find the area of the remaining part of cardboard.

Q45 Due to heavy floods in a state, thousands were rendered homeless. 200 schools collectively offered to the state government to provide place and the canvas for 1000 tents to be fixed by the government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 4.8 m and height 3m, with conical upper part of same base radius but of height 2 m. If the canvas used to make the tents costs 150 per sq.m, find the amount shared by each school to set up the tents.

Q46 The height of a cone is 30cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be $\frac{1}{125}$
of the volume of original cone, determine at what height above the base the section is made.

Q47 A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 40 cm and height 25 cm which are filled completely. Find the diameter of the cylindrical vessel.

Q48 An iron spherical ball has been melted and recast into smaller balls of equal size. The radius of each of the smaller balls is one-third of the radius of the original ball. Compare the surface area of all the smaller balls combined together with that of the original ball.

Q49 A path 3 m wide surrounds a circular pond of diameter 60 m. How many cubic meters of gravel are required to grave the path to a depth of 25 cm?

Q50 A well of diameter 8 m is dug 24m deep. The earth taken out of it is evenly spread all around it to form an embankment of height 80 cm. Find the width of the embankment?