26/03/2020Mensuration(Study by Topics Senior Class) 0Comments by Gate Academy Welcome to your Mensuration(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. The diagram shows a prism which has as its cross-section a trapezium with the dimensions indicated. If the prism is 10 cm long, its volume is 480 cm³960 cm³720 cm³360 cm³2. Two walls and the ceiling of a room meet at right angles at point P. A fly is in the air, 1 meter from one wall, 8 meters from the other wall and 9 meters from the point P. How many meters is the fly from the ceiling?2415143. What fraction of the area of a regular hexagon is the area of regular hexagon obtained by joining the midpoints of the sides of the first hexagon in order?3/41/21/42/34. Five marbles of various sizes are placed in a conical funnel. Each marble is in contact with the adjacent marble(s).Also, each marble is in contact all around the funnel wall. The smallest marble has a radius of 8 mm. The largest marble has a radius of 18 mm. What is the radius (in mm) of the middle marble?111012155. In the figure below, ABCDEF is a regular hexagon and ∠∠ AOF =90∘=90∘ . FO || EDED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?1/181/61/121/246. One of the sides of a rectangle measures 5 cm and the diagonal is 13 cm long. The area of the rectangle is30 cm232.5 cm260 cm265 cm27. A sector of a circle is bounded by two radii each of length 14cm and an arc of length 12 cm. The area of the sector is168 cm square84 cm square42 cm square63 cm square8. Find the dimensions of the rectangle that has a length 3 meters more that its width and a perimeter equal in value to its area?W = 1, L = 3W = 2, L =4w = 3, L = 6W = 5, L = 69. In a bullet the gun powder is to be filled up inside the metallic enclosure. The metallic enclosure is made up of a cylindrical base and conical top with the base of radius 5 cm. The ratio of height of cylinder and cone is 3 : 2. A cylindrical hole is drilled through the metal solid with height two-third the height of metal solid. What should be the radius of the hole, so that the volume of the hole (in which gun powder is to be filled up) is one-third the volume of metal solid after drilling?33π cm√(88/5) cm55/8 cm√(55/8) cm10. Water flows at the rate of 10 metres/minute from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cms and depth 24 cms?55 min51 min48 min52 min11. An equilateral triangle circumscribes all the six circles, each with radius 1 cm. What is the perimeter of the equilateral triangle?12(√3+4) cm6(2+√3) cm3(√3+2) cm6(2-√3) cm12. In the diagram, O is the center with radius 7 cm and <QPR = 30°. Find the length of arc QR (Take π = 22/7) 22/3 cm12 cm11/3 cm21/2 cm13. The area of an equilateral triangle of side 8 cm is36√3 cm²16√3 cm²32√3 cm²48 cm²14. A rectangular pool 20 m wide and 60 m long is surrounded by a walkway of uniform width. If the total area of the walkway is 516m2,how wide, in metres, is the walkway?4.3 m3 m43 m3.5 m15. A storage tank in the shape of a cuboid of base 2.5 m by 2m can hold up to 7,500 litres of water. The height of the tank is0.15 m1.0 m0.75 m1.5 m16. Three identical cones with base radius r are placed on their base so that each is touching the other two. The radius of the circle drawn through their vertices is  smaller than rdepends on the height of the conesmaller than rlarger than requal to r17. Find the circumference of a circular disk whose area is 100 π square centimeters20π19π24π22π18. Find the total surface area of a closed cylindrical container with radius 5 cm and a height of 34 cm.220π sq. cm390π sq. cm130π sq. cm320π sq. cm19. Find the volume of a closed cylindrical container with radius 5 cm and a height of 34 cm.850π cubic cm950π cubic cm704 cubic cm450π cubic cm20. In the diagram, PQR and RST are two semicircles with diameters 7 cm and 3.5 cm respectively and PT = 3.5 cm respectively and PT = 3.5 cm.The perimeter of the figure is23.5 cm16.5 cm14 cm20 cm21. Let ABCDEF be a regular hexagon. What is the ratio of the area of the ΔACEΔACE to that of the hexagon ABCDEF?2/31/25/61/322. A piece of string is wound uniformly around a triangular prism ABCDEF, of an equilateral base. The thread starts from the corner A at the base and ends at the corner D of the top, as shown in the figure. If there are total 14 rounds of string and the side of the base and the height of the prism are 2 cm and 13 cm respectively, then find the length of the string.84 cm85 cm87 cm97 cm23. A regular hexagonal prism has its perimeter of bases as 144 cm and height 120 cm. It contains water upto a height of 110 cm. A spherical ball of diameter of 35 cm is dropped into it due to which the level of water rises and some water flows out. Find the volume of water that flows out.9000 cc2000 cc7500 cc11000 cc24. Two triangles have the same area ifthe three sides of one are equal to the three sides of the otherthe three angles of one are equal to the three angles of the otherthey lie between the same parallelsthey are similar25. The angle of a sector of diameter 12 cm is 75°. Find the area of the sector129/7 cm²176/7 cm²82/7 cm²165/7 cm²26 out of 25Time is Up!