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 2.8m, find the area of the canvas used for making the tent.Find the cost of the canvas of the tent at the rate of Rs.500 per m².Also find the volume air enclosed in the tent.

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.

Water flows out through a circular pipe whose internal radius is 1 cm, at the rate of 80 cm/second into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour?

Metal spheres, each of radius 2 cm are packed into a rectangular box of internal dimensions 16 cm x 8 cm x 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of the liquid. [Use \(\pi\) = 3.14]

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.)

The given figure shows a tent which is made in the form of a frustum of a cone surmounted by another cone. The diameters of the base and the top of the frustum are 20 m and 6 m respectively and the height is 24 m. If the height of the tent is 28 m and the radius of the conical part is equal to the radius of the top of the frustum, find the quantity of canvas required.

An iron sphere of radius a units is immersed completely in water contained in a right circular cone of semi-vertical angle 30^o , water is drained off from the cone till its surface touches the sphere. Find the volume of water remaining in the cone.

An empty cylindrical container of radius 7 m and height 10 m is covered by a conical cap of radius 10.5 m and height 9 m. Calculate the volume of the air trapped inside.

The patients in a hospital are given soup daily in a cylindrical bowl of diameter 7 cm. On a particular day, the girls of kanya Mahavidyalaya decided to cook the soup for the patients.
(i) If they fill the bowl with soup to a height of 5 cm, then how much soup is to be cooked for 300 patients?
(ii) Which value is depicted by the girls?