A wooden article was made by scooping out a hemisphere from each end of a solid cylinder.If the height of the cylinder is 20cm and radius of the base is 3.5cm, find the total surface area of the article.

A juice seller serves his customers using a glass as shown in figure.The inner diameter of the cylindrical glass is 5cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass.If the height of the glass is 10cm, find the apparent capacity of the glass and its actual capacity.[\(\pi\)=3.14]

A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter of the sphere.

A tent consists of a frustum of cone, surmounted by a cone. If the diameter of the upper and lower circular ends of the frustum are 14 m and 26 m respectively, the height of the frustum is 8 m and the slant height of the surmounted conical portion is 12 m, find the area of canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal.)

A lead pencil consists of a cylinder of wood with solid cylinder of graphite filled into it. The diameter of the pencil is 7 mm; the diameter of the graphite is 1 mm and the length of the pencil is 10 cm. Calculate the weight of the whole pencil if the specific gravity of the wood is 0.7 g/cm³ and that of the graphite is 2.1 g/cm³ .

Length of a room is one and half times of its breadth. The cost of carpeting the room at Rs.3.25 per m² is Rs.175.50 and the cost of papering the walls at Rs.1.40 per m² is Rs.240.80. If 1 door and 2 windows occupy 8 m², find the dimensions of the room.

Water is flowering at the rate of 2.52 km/h through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40 cm, If the increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter of the pipe.

A shuttlecock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere as shown in the figure. The external diameters of the frustum are 6 cm and 2 cm and the height of the entire shuttle cock is 7 cm. Find the external surface area.

A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the bucket if the cost of metal sheet used is Rs. 15 per 100 cm² and find the cost of the milk which can completely fill the bucket at the rate of Rs. 16 per litre. \([Use\quad \pi =3.14]\)

A tank is 225 m long, 162 m broad. With what velocity per sec must water flow into it through an aperture 60 cm by 45 cm that the level may be raised by 20 cm in 5 h?