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. 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 cmn/h² cmh/n² cm2. 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 cm5 cm7.5 cm10 cm3. Find the area of the shaded region.270 sq. cm175 sq. cm73 sq. cm208 sq. cm4. In the figure below, ABCDEF is a regular hexagon and ∠∠ AOF =90∘=90∘ . FO || EDED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?1/241/121/61/185. A string of length 66 cm is shaped into an arc of a circle of radius 28 cm. The angle of the sector is135 degrees90 degrees120 degrees45 degrees6. 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 is0.75 m0.15 m1.0 m1.5 m7. 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/3110π/3100π/3120π/38. 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?2141549. 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 rectangle1200500030001200010. 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 is8:112:34:73:511. ABCDEF is a regular hexagon of side 6 cm. What is the area of triangle BDF?32√3 cm²24 cm²27√3 cm²22 cm²12. 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 is63 cm square84 cm square42 cm square168 cm square13. 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 is8.8 cm2.2 cm6.0 cm4.4 cm14. The two parallel sides of a trapezium are 4 cm and 8 cm and are separated by a distance of 5 cm. The area of the trapezium is20 cm²60 cm²40 cm²30 cm²15. 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 cm20 cm15 cm28 cm16. 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?100 m, 15100 m, 16120 m, 15120 m, 1617. 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 is540 cm31500 cm3864 cm3900 cm318. The surface area of a sphere of radius 3.5 cm is take (π = 22/7)154 cm2616 cm2308 cm2179 2/3 cm219. 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 rdepends on the height of the conelarger than requal to rsmaller than r20. Find the circumference of a circular disk whose area is 100 π square centimeters20π22π19π24π21. 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?134222. 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.22 m²168 m²42 m²84 m²23. 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?3.82.53.5424. A cylindrical metal pipe of wall thickness 1 cm has an internal radius of 15cm. The volume of metal per meter of pipe is29π cm32,900π cm331π cm33,100π cm325. A rectangular pool 20 m wide and 60 m long is surrounded by a walkway of uniform width. If the total area of the walkway is 516m^{2,}how wide, in metres, is the walkway?4.3 m3.5 m43 m3 m26 out of 25Time is Up!