26/03/2020 Mensuration(Study by Topics Senior Class) 0Comments by Gate Academy Welcome to your Mensuration(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. A circular paper is folded along its diameter, then again it folded to form a quadrant. Then it is cut as shown in the figure, after it the paper was reopened in the original circular shape. Find the ratio of the original paper to that of the remaining paper? (The shaded portion is cut off from the quadrant. The radius of quadrant OAB is 5 cm and radius of each semicircle is 1 cm)25 : 1611: 1725 : 920 : 92. 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?1415423. Let ABCDEF be a regular hexagon. What is the ratio of the area of the ΔACEΔACE to that of the hexagon ABCDEF?1/22/35/61/34. A 32 cm long string just fits around the perimeter of a square board. The area of the board is144 cm²32 cm²100 cm²64 cm²5. If the sides of each square is 10. Find the area of shaded region1510080756. 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 cc7500 cc9000 cc2000 cc7. 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 > t > cs > c > tc > s > tc > t > s8. 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  smaller than rsmaller than rdepends on the height of the conelarger than requal to r9. Consider a cylinder of height h cm and radius 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 cmh/n cmh/n² cmn/h² cm10. 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 be90.592.585.587.511. 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 is900 cm3864 cm31500 cm3540 cm312. The material within a hollow sphere of internal and external diameters 4 cm and 8 cm respectively, is melted and cast into the form of a right circular cone of base diameter 8 cm. Find the height of the cone.14 cm15 cm20 cm28 cm13. Consider a cylinder of height h cm and radius 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 nh= √2nh =√13nh = √17nh = n14. Find the area of the shaded region in the given figure of square ABCD148 cm²192 cm²128 cm²128 cm²15. Find the area of the shaded region.175 sq. cm73 sq. cm208 sq. cm270 sq. cm16. The area of the trapezium PQRS in the figure is36 cm²18√3 cm²36√3 cm²72 cm²17. The semicircle of area 1250 π centimeters is inscribed inside a rectangle. The diameter of the semicircle coincides with the length of the rectangle. Find the area of the rectangle1200050003000120018. Neeraj has agreed to mow a lawn, which is a 20 m × 40 m rectangle. He mows it with 1 m wide strip. If Neeraj starts at one corner and mows around the lawn toward the centre, about how many times would he go round before he has mowed half the lawn?184.108.40.20619. 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, is2/√(2-1)2/ √(2+1)√2/ √2+1√2 / √(2-1)20. The total surface area of a cone of base radius 3 cm and height 4 cm istake (π = 22/7)66 cm2103 5/7 cm275 3/7 cm237 5/7 cm221. 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 cot 30°) cm(5 tan 30°) cm(5 sin 30°) cm22. 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 is440 cm2748 cm2594 cm2208 cm223. Find the area of the quadrilateral shown in the figure.22516914412624. 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 $100 to paint one square meter$ 102$ 86$ 600$ 85525. 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?2563753003726 out of 25Time is Up!