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. 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 45:4 75:16 5:36 25:48 2. 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 20 sq. cm 10 sq. cm 15 sq. cm 12 sq. cm 3. 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 748 cm2 208 cm2 594 cm2 440 cm2 4. 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 28/3 cm 14/3 cm 14 cm 7/2 cm 5. 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? 245π 5245π 5425π 254π 6. 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 equal to the side of the cube √3 times the side of the cube 1/√3 times the side of the cube 7. Let ABCDEF be a regular hexagon. What is the ratio of the area of the <span id="MathJax-Element-93-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="ΔACE">ΔACEΔACE to that of the hexagon ABCDEF? 2/3 1/3 1/2 5/6 8. 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 10/3 5/3 9. 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) cm √(55/8) cm 55/8 cm 10. The figure shows a rectangle of dimensions 3x by 2x. The shaded portion of uniform width 2 cm, has an area of 64 cm². Find the value of x 4 cm 8 cm 6 cm 7 cm 11. 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, find the cost to the nearest dollar of painting the box if it costs $100 to paint one square meter $ 600 $ 855 $ 102 $ 86 12. In the triangle PQR shown 36 cm² 72 cm² 108 cm² 144 cm² 13. 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 1/2 14. A cone of height 12 cm has a volume of 330 cm³. The volume of a cone wih the same radius but of height 8cm is 220 cm3 300 cm3 146 2/3 cm3 270 cm3 15. 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. 97 cm 87 cm 85 cm 84 cm 16. 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 17. Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be 92.5 85.5 87.5 90.5 18. 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? 12 10 15 11 19. 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 6.0 cm 2.2 cm 4.4 cm 8.8 cm 20. A string of length 66 cm is shaped into an arc of a circle of radius 28 cm. The angle of the sector is 45 degrees 90 degrees 135 degrees 120 degrees 21. One of the sides of a rectangle measures 5 cm and the diagonal is 13 cm long. The area of the rectangle is 60 cm2 30 cm2 32.5 cm2 65 cm2 22. 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 19.4 cm 15.2 cm 11 cm 16.8 cm 23. Consider a cylinder of height h cm and radius <span id="MathJax-Element-70-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). The same string, when wound on the exterior four walls of a cube of side n cm, starting at point C and ending at point D, can give exactly one turn (see figure, not drawn to scale). The length of the string is √13n cm √2n cm √17n cm n cm 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 0.75 m 1.0 m 1.5 m 0.15 m 25. 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? 14 2 15 4 1 out of 25 Time is Up! Time's up