Page 1 :
CYLINDERS, CYLINDER Solids like circular pillars, circular pipes, circular pencils,, measuring jars, road rollers and gas cylinders, etc., are said to be in, , cylindrical shapes., Formulae:, Let us consider a cylinder whose height is h units and the radius of, whose base is r units. Then, we have:, ), , Volume of the cylinder = (rr h) cubic units., , (i) Curved surface area of the cylinder = (27trh) sq units., , (ii) Total surface area of the cylinder, , (area of curved surface) + 2(base area), (27trh +2tr) sq units., =, , HOLLOW CYLINDERS Solids like iron pipes, rubber tubes, etc., are in the shape, of hollow cylinders., , Formulae:, For a hollow cylinder with external radius R units, internal radius r, units and height (or length) h units, we have:, i) Volume of material = (exterior volume) - (interior volume), =, , (TR°h tr h) cubic units., -, , (i) Curved surface area = (external surface) + (internal surface), , (27tRh + 21trh) sq units., (ii) Total surface area =(curve surface) + 2(area of base ring), , [(2Rh +2n7h)+2(TR-nr)]sq units.

Page 2 :
How many cubic metres of earth must be dug out to sink a well, 14 m deep and having a radius of 4 m? If the earth taken out is, , spread over a plot of dimensions (25 mX 16 m), what is the height, of the platform so formed?, SOLUTION, , Clearly, we have r =4m and h = 14 m., , Volume of the earth dug out of the well, , =(nr h) cubic units = ( x 4x4x14) m'= 704 m?., Area of the given plot = (25 x 16) m2 = 400 m?., Volume of the platform formed = volume of the earth dug out, , 704 m., Height of the platform=Volumein m, area in m*, , (704, 400 m=0 m1.76 m., Hence, the height of the platform so formed = 1.76 m., , A well of inner diameter 14 m is dug to a depth of 15 m. Earth taken, out of it has been evenly spread all around it to a width of 7 m to, form an embankment. Find the height of the embankment so formed., SOLUTION, , Radius of the well, r= 7m, and its depth, h = 15 m., , Volume of the earth dug out, , kmen, , Embank, , volume of the well, = (Ttr h) cubic units, , Well, , -x77x15) m= 2310 m., , Secondary School Mathematics for Class 9, Width of the embankment = 7 m., External radius of the embankment = (7+7) m = 14 m., , Internal radius of the embankment = 7 m., , Area of the embankment, , =, , t x, , [(14)-7] m, , 04+7x14-7mm, , -x21x7)m?-462mi, Volume of the embankment = volume of the earth dug out, , = 2310 m, , Height of the embankment, , (volume, of the embankment in m-(462 m=5m., area of the embankment in m2, Hence, the height of the embankment formed = 5 m.