Welcome to your Mensuration(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. 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 208 cm2 594 cm2 748 cm2 2. A sector of a circle of radius 14 cm which subtends an angle of 120° at the center is bent to form a cone. The base radius of the cone is 14/3 cm 14 cm 28/3 cm 7/2 cm 3. 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√2 4√2 2 √2 4. A hollow cylinder of base radius 7 cm and height 10 cm is closed at one end.If π = 22/7, then its volume is 440 cm3 70 cm3 1540 cm3 3080 cm3 5. The volume of a certain sphere is numerically equal to twice its surface area. The diameter of the sphere is 6 1/6 12 9 6. A right circular cone has a radius of 5 cm and a vertical angle of 60°. The height of the cone is (5 cos 30°) cm (5 sin 30°) cm (5 tan 30°) cm (5 cot 30°) cm 7. An arc of length 22 cm subtends an angle of 270° at the center of the circle.If π = 22/7, the radius of the circle is 4 2/3 cm 7 cm 9 1/3 cm 6 cm 8. The volumes of two solid spheres are 32 cm³ and 500 cm³. The ratio of their radii is 4 : 25 2 : 5 3 : 5 8 : 125 9. 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. 80π/3 100π/3 120π/3 110π/3 10. 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? 37 300 375 256 11. A farmer has decided to build a wire fence along one straight side of his property. For this, he planned to place several fence-posts at 6 m intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was 5 less than required. However, he discovered that the number of posts he had bought would be just sufficient if he spaced them 8 m apart. What is the length of the side of his property and how many posts did he buy? 120 m, 16 100 m, 16 120 m, 15 100 m, 15 12. All five faces of a regular pyramid with a square base are found to be of the same area. The height of the pyramid is 3 cm. The total area of all its surfaces is 10 sq. cm 20 sq. cm 15 sq. cm 12 sq. cm 13. An arc of a circle of radius 5.6 cm subtends an angle of 45° at the center of the circle. If π = 22/7, the length of the arc is 4.4 cm 2.2 cm 6.0 cm 8.8 cm 14. A cylindrical metal pipe of wall thickness 1 cm has an internal radius of 15cm. The volume of metal per meter of pipe is 29π cm3 3,100π cm3 31π cm3 2,900π cm3 15. Find the total surface area of a closed cylindrical container with radius 5 cm and a height of 34 cm. 320π sq. cm 220π sq. cm 390π sq. cm 130π sq. cm 16. 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? 15 12 10 11 17. Two triangles have the same area if they are similar the three sides of one are equal to the three sides of the other the three angles of one are equal to the three angles of the other they lie between the same parallels 18. The angle of a sector of diameter 12 cm is 75°. Find the area of the sector 165/7 cm² 129/7 cm² 176/7 cm² 82/7 cm² 19. 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 20/3 5/3 5 10/3 20. 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? 1/6 1/18 1/12 1/24 21. A cone of height 12 cm has a volume of 616 cm³, If π = 22/7, the radius of the cone is 3.5 cm 10.5 cm 14 cm 7 cm 22. 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 23. 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 5245π 245π 254π 24. 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 0.15 m 1.5 m 0.75 m 1.0 m 25. 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 2000 cc 9000 cc 7500 cc 1 out of 25 Time is Up! Time's up