Welcome to your Mensuration(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle, and square are c, t and s, respectively. Then, s > c > t s > t > c c > t > s c > s > t 2. 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 440 cm2 594 cm2 748 cm2 208 cm2 3. 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? 1/18 1/24 1/6 1/12 4. ABCDEF is a regular hexagon of side 6 cm. What is the area of triangle BDF? 32√3 cm² 24 cm² 22 cm² 27√3 cm² 5. 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 = 3, L = 6 W = 2, L =4 W = 5, L = 6 6. In the triangle PQR shown 108 cm² 144 cm² 72 cm² 36 cm² 7. In the figure, PQ//TS, TP//SQ, PQ = 4 cm, QR = 3 cm and RS = 6 cm. The ratio of the area of PQST to the area of PQRST is 2:3 4:7 3:5 8:11 8. 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? 4 1 3 2 9. A cow is tethered to one corner of a square field with side 20 m with a rope equal to the length of a side of the field. Another cow is tethered at the diagonally opposite corner with the grazing area just touching each other. What is the total grazing area? 100π(2 - √2) 200π(2 - √2) 200π(4 - √2) 150π(2 - √2) 10. PQRS is a parallelogram and ST is perpendicular to QR. If the area of triangle PSR is 25 cm² and|PS| = 10 cm, the length ST is 2.5 cm 5 cm 10 cm 7.5 cm 11. Consider a cylinder of height h cm and radius <span id="MathJax-Element-75-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). In the set-up of the previous two questions, how is h related to n h= √2n h =√13n h = n h = √17n 12. 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 48 min 52 min 51 min 13. The angle of a sector of diameter 12 cm is 75°. Find the area of the sector 82/7 cm² 176/7 cm² 129/7 cm² 165/7 cm² 14. The volume of a certain sphere is numerically equal to twice its surface area. The diameter of the sphere is 9 1/6 6 12 15. 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 [1] smaller than r larger than r depends on the height of the cone smaller than r equal to r 16. Find the edge of the cube that can be inscribed in a cone with base diameter 12 cm and height 8 cm. 4.8 24/ 2√2 24/ 2√2+3 2 17. The radius of a cone is <span id="MathJax-Element-82-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="2">√22 times the height of the cone. A cube of maximum possible volume is cut from the same cone. What is the ratio of the volume of the cone to the volume of the cube? 2.25π 3.18π 2.35 1.45 18. ABCD is a parallelogram and DE is perpendicular to BC, |CD| = 10 CM, |CE| = 6 cm and |BE| = 7 cm. The area of the parallelogram is 104 cm² 65 cm² 70 cm² 130 cm² 19. Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m^{2} at the centre. Find the ungrazed area. 168 m² 84 m² 22 m² 42 m² 20. 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? 254π 5245π 245π 5425π 21. A square tile measures 20 cm by 20 cm. How many of such tiles will cover a floor measuring 5m by 4m 320 250 500 400 22. A string of length 66 cm is shaped into an arc of a circle of radius 28 cm. The angle of the sector is 90 degrees 135 degrees 45 degrees 120 degrees 23. 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? 2,000π cm3 2,288π cm3 288π cm3 1,712π cm3 24. The area of the trapezium PQRS in the figure is 18√3 cm² 36 cm² 72 cm² 36√3 cm² 25. 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 is 0.75 m 1.0 m 1.5 m 0.15 m 1 out of 25 Time is Up! Time's up