The dimensions of a Cinema Hall are 100 m, 60 m, and 15 m. How many persons can sit in the hall, if each requires 150 m3 of air?
The edges of three cubes of metal are 3 cm, 4 cm, and 5 cm. They are melted and formed into a single cube. Find the edge of the new cube.
Three cubes, whose edges are x cm, 8 cm, and 10 cm respectively, are melted and recast into a single cube of edge 12 cm. Find 'x'.
Three equal cubes are placed adjacently in a row. Find the ratio of the total surfaced area of the resulting in cuboid to that of the sum of the total surface areas of the three cubes.
The cost of papering the four walls of a room at 75 paise per square meter is Rs. 240. The height of the room is 5 meters. Find the length and the breadth of the room, if they are in the ratio 5 : 3.
A tank 20 m long, 12 m wide and 8 m deep is to be made of iron sheet. If it is open at the top. Determine the cost of iron-sheet, at the rate of Rs. 12.50 per meter, if the sheet is 2.5 m wide.
The square on the diagonal of a cube has an area of 1875 sq. cm. Calculate:
(i) The side of the cube.
(ii) The total surface area of the cube.
The following figure shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in centimeters. Assume that all angles in the figures are right angles.
A swimming pool is 40 m long and 15 m wide. Its shallow and deep ends are 1.5 m and 3 m deep respectively. If the bottom of the pool slopes uniformly, find the amount of water in liters required to fill the pool.
The cross-section of a tunnel perpendicular to its length is a trapezium ABCD as shown in the following figure; also given that:
AM = BN; AB = 7 m; CD = 5 m. The height of the tunnel is 2.4 m. The tunnel is 40 m long.
(i) The cost of painting the internal surface of the tunnel (excluding the floor) at the rate of Rs. 5 per m2 (sq. meter).
(ii) The cost of paving the floor at the rate of Rs. 18 per m2 .
Water is discharged from a pipe of cross-section area 3.2 cm2 at the speed of 5m/s. Calculate the the volume of water discharged:
(i) In cm3 per sec.
(ii) In litres per minute.
A hose-pipe of cross-section area 2 cm2 delivers 1500 liters of water in 5 minutes. What is the speed of water in m/s through the pipe?
The cross-section of a piece of metal 4 m in length is shown below. Calculate:
(i) The area of the cross-section;
(ii) The volume of the piece of metal in cubic centimeters. If 1 cubic centimeter of the metal weighs 6.6 g, calculate the weight of the piece of metal to the nearest kg.
The dimensions of a car petrol tank are 50 cm × 32 cm × 24 cm, which is full of petrol. If car's average consumption is 15 km per liter, find the maximum distance that can be covered by the car.
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