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 angle of a sector of a circle of radius 4.2 cm is 150°.If π = 22/7, the perimeter of the sector is 11 cm 19.4 cm 15.2 cm 16.8 cm2. Consider a right circular cone of base radius 4 cm and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of the cone. Find the largest possible total surface area (in sq. cm) of the cylinder. 120π/3 100π/3 80π/3 110π/33. A open cylindrical container has a base radius of 3.5 cm. If the ratio of the area of its base to that of its curved surface is 1 : 6, the height of the container is 1.75 cm 10.5 cm 3.5 cm 7.0 cm4. In the diagram, O is the center with radius 7 cm and <QPR = 30°. Find the length of arc QR (Take π = 22/7) 12 cm 22/3 cm 11/3 cm 21/2 cm5. The ratio of the heights of two circular cylinders is 1 : 3 and the ratio of their base radii is 5 : 4.The ratio of their volumes is 25:48 75:16 5:36 45:46. The angle of a sector of diameter 12 cm is 75°. Find the area of the sector 82/7 cm² 129/7 cm² 165/7 cm² 176/7 cm²7. A square tin sheet of side 12 inches is converted into a box with open top in the following steps. The sheet is placed horizontally. Then, equal-sized squares, each of side x inches, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If x is an integer, then what value of x maximizes the volume of the box? 2 1 3 48. 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 360 cm³ 960 cm³ 720 cm³ 480 cm³9. A square, whose side is 2 m, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in meters, is √2/ √2+1 2/√(2-1) √2 / √(2-1) 2/ √(2+1)10. 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.What is the area of the region PQRST enclosed by the figure, to the nearest whole number 24 cm² 96 cm² 48 cm² 193 cm²11. One of the sides of a rectangle measures 5 cm and the diagonal is 13 cm long. The area of the rectangle is 65 cm2 60 cm2 32.5 cm2 30 cm212. A 32 cm long string just fits around the perimeter of a square board. The area of the board is 32 cm² 64 cm² 100 cm² 144 cm²13. Find the volume of a closed cylindrical container with radius 5 cm and a height of 34 cm. 850π cubic cm 704 cubic cm 450π cubic cm 950π cubic cm14. One of the diagonals of a rhombus is 15 cm long. If the rhombus has an area of 60 cm², the length of the other diagonal is 4 cm 5 cm 8 cm 12 cm15. 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? 3/4 2/3 1/4 1/216. There is a vast grassy farm in which there is a rectangular building of the farmhouse whose length and breadth is 50 m and 40 m respectively. A horse is tethered at a corner of the house with a tether of 80 m long. What is the maximum area that the horse can graze? 5425π 254π 5245π 245π17. ABCD is a square. A circle is inscribed in the square. Also taking A, B, C, D (the vertices of square) as the centres of four quadrants, drawn inside the circle, which are touching each other on the midpoints of the sides of square. Area of square is 4 cm2 . What is the area of the shaded region? (4 - 3π/2) cm² (π - 2) cm² (2π - 4) cm² (4 - 2π) cm²18. Glass spheres (which submerge fully in water) of radius 7 mm are dropped into a cylindrical vessel containing some water. The diameter of the vessel is 14 cm. Find how many spheres have been dropped in it if the water level rises by 3.5 cm? 37 300 256 37519. An open, rectangular wooden box of internal depth 40 cm has a base of internal dimensions 50 cm by 30 cm. If the box is made of wood of thickness 1 cm, the total volume of wood in the box is 8,552 cm3 12,000 cm3 9,888 cm3 8,224 cm320. The ratio of the sides of two similar rectangular blocks is 5 : 3. If the volume of the smaller block is 324 cm³, that of the other block is 864 cm3 900 cm3 540 cm3 1500 cm321. 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 = 3 W = 5, L = 6 W = 2, L =4 w = 3, L = 622. A right circular cone has a radius of 5 cm and a vertical angle of 60°. The height of the cone is (5 cot 30°) cm (5 cos 30°) cm (5 tan 30°) cm (5 sin 30°) cm23. A hollow cylinder of base radius 7 cm and height 10 cm is closed at one end.If π = 22/7,then its surface area is 594 cm2 440 cm2 208 cm2 748 cm224. A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle? 4√2 2 √2 2√225. ABCDEF is a regular hexagon of side 6 cm. What is the area of triangle BDF? 24 cm² 22 cm² 27√3 cm² 32√3 cm²26 out of 25Time is Up!