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Syllabus
24. The cross-section Of a of metal 2m in length shown in the adjoining figure Calculate: (i) the area of its cross-section; (ii) the volume of piece of metal; (iii) the weight of piece of metal to the nearest kg, if 1 or the metal weighs 6.5g.
25. The adjoining figure shows the cross-section of a concrete wall to be constructed. It is 1.9 cm wide at the bottom, 90 cm wide at the top and 5 m high. If its length is 20 m, find • (i) the cross-sectional area; (ii) the volume of the concrete in the wall.
26. A square brass plate of side x cm is 1 mm thick and weighs 5.44 kg. If 1 cm^3 of brass weighs 8.5 g, find the value of x.
27. The area of cross-section of a rectangular pipe is 5.4 cm^2 and water is pumped out of it at the rate Of
27 kmph. Find, in litres, the volume of water which flows Out of the pipe in 1 minute.
Q3. 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. Calculate :
(i) the cost of painting the internal surface of the tunnel (excluding the floor) at the rate of Rs. 5 per m2 (sq. metre).
(ii) the cost of paving the floor at the rate of Rs. 18 prt m2.
Q4. Water is discharged from pipe of cross- section area 3.2 cm2 at the speed of 5 m/s. Calculate the volume of water discharged :
(i) in cm3 per sec.
(ii) in litres per minute.
Q.10. The following figure shows closed victory-stand whose dimensions are given in cm.
Find the volume and the surface area of the victory stand.
18. Find the volume of wood required for making the open box with external dimensions 17.5 cm long, 14 cm wide, 10 cm high, wood 7.5 mm thick.
Q.1. The following figure shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in centimetres.
Assume that all angles in the figure are right angles.
16. A tank 72 cm long, 60 cm wide, 36 cm high, contains water to a depth of 18 cm. A metal block 48 cm by 36 cm by 15 cm is put into the tank and totally submerged. Find the Water level Rises.
Q.16. The base of a right pyramid is a square, each side of which is 6 cm long and height is 4 cm. Find the total surface area of the pyramid in sq.cm.
Q.17. Find the canvas needed to cover a conical tent whose slant height is 25 ft and height is 24 ft.
Q.18. A solid metallic sphere of radius 15 cm is drawn into a wire of diameter 5 mm. Find the length of the wire. (in m)
Q. A box 3 m long, 62.5 cm wide and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the sheet of which box is made, determine :
(i) area of the sheet required to make the box.
(ii) the cost of sheet used at the rate of Rs. 200 per .
2. It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same ?
3. A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm (see fig. 13.11). Find its
(i) inner curved surface area,
(ii) outer curved surface area,
(iii) total surface area.
43. A solid cylinder of radius and height is vertically cut in to two equal parts, then the total surface area increased by _______
Q.4. A closed rectangular box has inner dimensions 90 cm.by 70 cm. Calculate its capacity and the area of tin foil needed to line to its inner surface.
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Q.7. A rectangular tank 30 cm 20 cm 12 cm contains water to a depth of 6 cm. A metal cube of side 10 cm is placed in the tank with its one face resting on the bottom of the tank. Find the volume of water, in litres, that must be poured in the tank so that the metal cube is just submerged in the water.
Q. Two cubes, whose length of edges are equal, are combined side by side to form a rectangular parallelepiped. If the area of whole surface of the rectangular parallelepiped is 360 sq. cm, then find the volume of each cube.
Q. Prove that the angle in a semicircle is a right angle.
Q. Prove that the opposite angles of a cylic quadrilateral are supplementary.
Q.2. Total surface area of a cuboid is 22 cm square its height is 1 m and breadth is 2 m. Find its length and volume.
Q. When a body has uniform cross-section, its surface area (excluding cross-section) = Perimeter of cross -section x length.. Explain the above lines/