26/03/2020 Mensuration(Study by Topics Senior Class) 26/03/2020 0Comments by Gate Academy Welcome to your Mensuration(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. In the figure below, ABCDEF is a regular hexagon and ∠AOF = 90°. FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF? 1/12 1/18 1/24 1/6 2. In the diagram, O is the center with radius 7 cm and <QPR = 30°. Find the length of arc QR (Take π = 22/7) 21/2 cm 11/3 cm 12 cm 22/3 cm 3. 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. 11000 cc 9000 cc 2000 cc 7500 cc 4. 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 12 cm 8 cm 4 cm 5 cm 5. In the above diagram, <span id="MathJax-Element-46-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="∠ABC=90∘=∠DCH=∠DOE=∠EHK=∠FKL=∠GLM=∠LMN">∠ABC=90∘=∠DCH=∠DOE=∠EHK=∠FKL=∠GLM=∠LMN∠ABC=90∘=∠DCH=∠DOE=∠EHK=∠FKL=∠GLM=∠LMN AB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MN The magnitude of ∠FGO = What is the ratio of the areas of the two quadrilaterals ABCD to DEFG? 1:2 7:12 12:7 2:1 6. 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 16.8 cm 15.2 cm 19.4 cm 7. 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. 87 cm 85 cm 97 cm 84 cm 8. A cylindrical container of radius 10cm and height 20cm is filled to the brim with water. A steel ball of radius 6cm is now dropped into the cylinder so that excess water flows out. How much water is left in the container? 1,712π cm3 288π cm3 2,288π cm3 2,000π cm3 9. Find the area of the shaded region in the given figure of square ABCD 148 cm² 128 cm² 192 cm² 128 cm² 10. A solid cone of metal of radius r and height h cm is melted into a cube of length a. If h + r = 10 cms, and the volume of the cube formed is maximum then the radius of the cone in cms is 5 20/3 5/3 10/3 11. 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 min 51 min 48 min 52 min 12. One of the two parallel sides of a trapezium is one-half the length of the other.If the height of the trapezium is 7 cm and its area is 52.5 cm², the length of the parallel sides are 2.5 cm, 5 cm 5 cm, 10 cm 7.5 cm, 15 cm 10 cm, 20 cm 13. 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 748 cm2 440 cm2 208 cm2 14. 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 is 63 cm square 168 cm square 42 cm square 84 cm square 15. If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be √3 times the side of the cube 1/√3 times the side of the cube equal to the side of the cube 3 times the side of the cube 16. 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? 256 375 37 300 17. Consider a cylinder of height h cm and radius <span id="MathJax-Element-66-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="r=2π">r=2πr=2π cm as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of n turns (in other words, the string’s length is the minimum length required to wind n turns). What is the vertical spacing between the two consecutive turns? h/√n cm h/n cm n/h² cm h/n² cm 18. 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) 19. 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? 11 15 12 10 20. 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 16.8 cm 15.2 cm 11 cm 19.4 cm 21. 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? 1/2 1/4 2/3 3/4 22. 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? 2 4√2 √2 2√2 23. The total surface area of a cone of base radius 3 cm and height 4 cm istake (π = 22/7) 66 cm2 75 3/7 cm2 103 5/7 cm2 37 5/7 cm2 24. In the figure below, ABCDEF is a regular hexagon and <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="∠">∠∠ AOF <span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="=90∘">=90∘=90∘ . FO || <span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="ED">EDED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF? 1/18 1/12 1/6 1/24 25. The area of an equilateral triangle of side 8 cm is 32√3 cm² 48 cm² 16√3 cm² 36√3 cm² 1 out of 25 Time is Up! Time's up