SELINA SOLUTIONS MATHS CLASS 10 CHAPTER 20 EX 20 G CYLINDER, CONE AND SPHERE

VIDEO SOLUTIONS

10. A cylimirical water tank of diameter 2-8 m and height 4.2 m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4 m Calculate, in minutes, the time it takes to fill the tank

11. Water flows. at 9 km per hour. through a cylindrical pipe of cross-sectional area 25 cm2. If this water is collected into a rectangular cistern of dimensions 7.5 m by 5 m by 4 m: calculate the rise in level in the cistern in 1. hour 15 minutes.

12.The given figure shows the cross-section of a cone. a cylinder and a hemisphere all with the same diameter 10 cm, and the other dimensions are as shown.
Calculate : (a) the total surface area, (b) the total volume of the solid and (c) the density of the material it its total weight is 1.7 kg.

13. A solid, consisting of a right circular cone standing on a hemisphere, is placed upright in a right circular cylinder, full of water. and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of cone is 4 cm. Give your answer to the nearest cubic centimetre.

14 A metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m. Calculate : (i) the total area of the internal surface. excluding the base: (ii) the internal volume of the container in m3.

15. An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85 m and height of the cylindrical part is 50 m. If the diameter of the base is 168 m, find the quantity of canvas required to make the tent. Allow 20% extra for fold and for stitching. Give your answer to the nearest m2.
[2001]

16. A test tube consists of a hemisphere and a cylinder of the same radius. The volume of the water required to fill the whole tube is 4235 15 9 5 , 6 cm', and 6 cm3 of water is required to fill the tube to a level which is 4 cm below the top of the tube. Find the radius of the tube and the length of its cylindrical pan_

17. A solid is in the form of a right circular cone mounted on a hemisphere. The diameter of the base of the cone, which exactly coincides with hemisphere, is 7 cm and its height is 8 cm. The solid is placed in a cylindrical vessel of internal radius 7 cm and height 10 cm. How much water, in cm', will be required to fill the vessel completely ?

18. Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height S cm. Find Abe radius of the cone so formed. 120151

19. A certain number of metallic cones, each of radius 2 cm and height 3 cm, are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used. [2016]

20. A conical tent is to accommodate 77 persons. Each person must have 16 f►i3 of air to breathe. Given the radius of the tent as 7 III, find the height of the tent and also its cursed surface area. 12017]