Welcome to your Mensuration(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. 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 cm 2. An equilateral triangle circumscribes all the six circles, each with radius 1 cm. What is the perimeter of the equilateral triangle? 6(2-√3) cm 12(√3+4) cm 6(2+√3) cm 3(√3+2) cm 3. 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 : 9 25 : 16 20 : 9 11: 17 4. 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? 1 3 2 4 5. The volume of a cone of radius 6 cm and vertical height 7 cm is take (π= 22/7) 26.4 cm3 264 cm3 21 cm3 42 cm3 6. If the sides of each square is 10. Find the area of shaded region 80 75 15 100 7. 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 equal to the side of the cube 3 times the side of the cube √3 times the side of the cube 1/√3 times the side of the cube 8. 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 2.5 cm, 5 cm 10 cm, 20 cm 5 cm, 10 cm 7.5 cm, 15 cm 9. 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. 2000 cc 11000 cc 9000 cc 7500 cc 10. 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 11. A 32 cm long string just fits around the perimeter of a square board. The area of the board is 144 cm² 100 cm² 32 cm² 64 cm² 12. 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 10 cm² 14 cm² 12 cm² 16 cm² 13. 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? 120 m, 15 100 m, 16 120 m, 16 100 m, 15 14. In the figure below, ABCDEF is a regular hexagon and <span id="MathJax-Element-1-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="∠">∠∠ AOF <span id="MathJax-Element-2-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="=90∘">=90∘=90∘ . FO || <span id="MathJax-Element-3-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="ED">EDED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF? 1/6 1/18 1/24 1/12 15. If a cube of maximum possible volume is cut off from a solid sphere of diameter d, then the volume of the remaining (waste) material of the sphere would be equal to π - d d³/3 (π/2 - 1/√3) d³/4 (√2 - π) d³/3 (π - d/2) 16. The diagram shows a prism which has as its cross-section a trapezium with the dimensions indicated. If the prism is 10 cm long, its volume is 720 cm³ 480 cm³ 960 cm³ 360 cm³ 17. Find the area of the quadrilateral shown in the figure. 225 169 126 144 18. Consider a cylinder of height h cm and radius <span id="MathJax-Element-75-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). In the set-up of the previous two questions, how is h related to n h =√13n h = √17n h= √2n h = n 19. The area of the triangle shown is 5 cm². The angle a is 60° 45° 30° 90° 20. 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? r (1+√5) 2r+√3 2r (1+√3) 2r (2+√3) 21. ABCD is a square. A circle is inscribed in the square. Also taking A, B, C, D (the vertices of square) as the centres of four quadrants, drawn inside the circle, which are touching each other on the midpoints of the sides of square. Area of square is 4 cm^{2} . What is the area of the shaded region? (4 - 2π) cm² (π - 2) cm² (4 - 3π/2) cm² (2π - 4) cm² 22. 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? 1/18 1/24 1/12 1/6 23. 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 rectangle 12000 3000 1200 5000 24. In the diagram, PQR and RST are two semicircles with diameters 7 cm and 3.5 cm respectively and PT = 3.5 cm respectively and PT = 3.5 cm.The perimeter of the figure is 20 cm 16.5 cm 14 cm 23.5 cm 25. 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. 84 cm 85 cm 87 cm 97 cm 1 out of 25 Time is Up! Time's up