Tiêu đề Notes_Surface Area and Volume_Surface Area and Volume.pdf ✅

4 Ex.4. A room is half as long again as it is broad. The cost of carpeting the room at Rs 18 per m2 is Rs 972 and the cost of white-washing the four walls at Rs 6 per m2 is Rs 1080. Find the dimensions of the room. Sol. Let breadth = (x) in. Then, length = ) 2 3 (  m. Let height of the room = y m. Area of the floor = 2 54 18 972 m Rate colt of carpeting                54 2 3 x  x   36 6 3 2 54 2          x   x . So, breadth = 6 m and length =       6 2 3 m = 9 m. Now, area of four walls = 2 2 180 6 cos 1080 m m Rate t of white washing                .  6 30 180 2(9 6) 180 30 180          y   y   y  . Hence, length = 9 m, breadth = 6 m, height = m. Ex.5. The water in a rectangular reservoir having a base 80 x m 60 m, is 6.5 m deep. In what time can the water be emptied by a pipe of which the cross section is a square of side 20 cm, if water runs through the pipe at the rate of 15 km/ hr ? Sol. Volume of water in the reservoir = (80 x 60 x 6.5) m3 = 31200 m3 . Area of cross section of the pipe = 3 2 25 1 100 20 100 20 m  m       . Volume of water emptied in 1 hr = 3 3 15000 600 25 1  m  m       . Time taken to empty the reservoir =       600 31200 hrs = 52 hrs. RIGHT CIRCULAR CYLINDER Solids like circular pillars, circular pencils, measuring jars, road rollers and gas cylinders, etc., are said to be in cylindrical shape. In mathematical terms, a right circular cylinder is a solid generated by the revolution of a rectangle about its sides. Let the rectangle ABCD revolve about its side AB, so as to describe a right circular cylinder as shown in the figure. You must have observed that the cross-section of a right circular cylinder are circles congruent and parallel to each other. Lateral Surface (curved surface) Bottom End Top End