Welcome to your Mensuration(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. 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? 2.35 1.45 2.25π 3.18π2. Find the volume of a closed cylindrical container with radius 5 cm and a height of 34 cm. 450π cubic cm 850π cubic cm 704 cubic cm 950π cubic cm3. 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 5:36 45:4 75:16 25:484. 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, is √2 / √(2-1) 2/√(2-1) √2/ √2+1 2/ √(2+1)5. 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 r smaller than r depends on the height of the cone larger than r equal to r6. 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 15.2 cm 16.8 cm 19.4 cm 11 cm7. 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. 87 cm 85 cm 84 cm 97 cm8. The area of the triangle shown is 5 cm². The angle a is 30° 45° 90° 60°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? 55/8 cm √(88/5) cm 33π cm √(55/8) cm10. 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, the total volume of wood in the box is 9,888 cm3 12,000 cm3 8,224 cm3 8,552 cm311. 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 5/3 20/3 5 10/312. The surface area of a sphere of radius 3.5 cm is take (π = 22/7) 616 cm2 308 cm2 179 2/3 cm2 154 cm213. A string of length 66 cm is shaped into an arc of a circle of radius 28 cm. The angle of the sector is 120 degrees 45 degrees 135 degrees 90 degrees14. One of the two parallel sides of a trapezium is one-half the length of the other.If the height of the trapezium is 7 cm and its area is 52.5 cm², the length of the parallel sides are 10 cm, 20 cm 5 cm, 10 cm 2.5 cm, 5 cm 7.5 cm, 15 cm15. In a trapezium PQRS, PQ//SR, |PQ| = 5 cm, |SR| = 7 cm and the trapezium has an area of 24 cm². The area of the triangle PQS is 12 cm² 14 cm² 10 cm² 16 cm²16. 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 7/2 cm 28/3 cm 14 cm17. If the sides of each square is 10. Find the area of shaded region 100 15 80 7518. One of the diagonals of a rhombus is 15 cm long. If the rhombus has an area of 60 cm², the length of the other diagonal is 8 cm 12 cm 5 cm 4 cm19. P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR? 2r+√3 2r (1+√3) r (1+√5) 2r (2+√3)20. The angle of a sector of diameter 12 cm is 75°. Find the area of the sector 176/7 cm² 165/7 cm² 82/7 cm² 129/7 cm²21. 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 8 cm 7 cm 6 cm 4 cm22. 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 is 4:7 2:3 8:11 3:523. In the above diagram, ∠ABC=90∘=∠DCH=∠DOE=∠EHK=∠FKL=∠GLM=∠LMN∠ABC=90∘=∠DCH=∠DOE=∠EHK=∠FKL=∠GLM=∠LMNAB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MNThe magnitude of ∠FGO =What is the ratio of the areas of the two quadrilaterals ABCD to DEFG? 12:7 2:1 7:12 1:224. A cone of height 12 cm has a volume of 616 cm³, If π = 22/7, the radius of the cone is 14 cm 7 cm 3.5 cm 10.5 cm25. In the triangle PQR shown 108 cm² 144 cm² 36 cm² 72 cm²26 out of 25Time is Up!