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).In the set-up of the previous two questions, how is h related to nh= √2nh =√13nh = √17nh = n2. 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 beequal to the side of the cube3 times the side of the cube1/√3 times the side of the cube√3 times the side of the cube3. Find the edge of the cube that can be inscribed in a cone with base diameter 12 cm and height 8 cm.24/ 2√2+324/ 2√224.84. 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?200π(2 - √2)150π(2 - √2)200π(4 - √2)100π(2 - √2)5. 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?12346. An equilateral triangle circumscribes all the six circles, each with radius 1 cm. What is the perimeter of the equilateral triangle?12(√3+4) cm3(√3+2) cm6(2+√3) cm6(2-√3) cm7. 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 x4 cm8 cm7 cm6 cm8. If the sides of each square is 10. Find the area of shaded region8015100759. The radius of a cone is √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?2.25π1.453.18π2.3510. 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?52 min51 min48 min55 min11. Let ABCDEF be a regular hexagon. What is the ratio of the area of the ΔACEΔACE to that of the hexagon ABCDEF?5/61/31/22/312. 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?3753002563713. 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?1/121/241/61/1814. 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 5 cm7.5 cm2.5 cm10 cm15. A open cylindrical container has a base radius of 3.5 cm. If the ratio of the area of its base to that of its curved surface is 1 : 6, the height of the container is1.75 cm10.5 cm3.5 cm7.0 cm16. Find the area of the shaded region in the given figure of square ABCD128 cm²192 cm²148 cm²128 cm²17. 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?3 m43 m4.3 m3.5 m18. The surface area of a sphere of radius 3.5 cm is take (π = 22/7)179 2/3 cm2154 cm2308 cm2616 cm219. 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 is45:45:3675:1625:4820. 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 is3:52:38:114:721. A cone of height 12 cm has a volume of 616 cm³, If π = 22/7, the radius of the cone is3.5 cm7 cm14 cm10.5 cm22. 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,c > t > sc > s > ts > c > ts > t > c23. Find the volume of a closed cylindrical container with radius 5 cm and a height of 34 cm.704 cubic cm450π cubic cm850π cubic cm950π cubic cm24. In the triangle PQR shown 36 cm²144 cm²72 cm²108 cm²25. 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?1210151126 out of 25Time is Up!