Welcome to your Mensuration(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. 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 3(√3+2) cm 12(√3+4) cm 6(2+√3) cm 2. A right circular cone has a radius of 5 cm and a vertical angle of 60°. The height of the cone is (5 cot 30°) cm (5 cos 30°) cm (5 sin 30°) cm (5 tan 30°) cm 3. A square tile measures 20 cm by 20 cm. How many of such tiles will cover a floor measuring 5m by 4m 250 400 500 320 4. A circular hall, surmounted by a hemispherical roof, contains 5236<span id="MathJax-Element-50-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="m3">m3m3 of air and the internal diameter of the room is equal to the height of the highest point of the roof above the ground. Find the height of the room (Take <span id="MathJax-Element-51-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="π=3.1416)">π=3.1416)π=3.1416) . 20 m 15 m 12 m 10 m 5. 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? √(88/5) cm √(55/8) cm 33π cm 55/8 cm 6. 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 is 540 cm3 1500 cm3 864 cm3 900 cm3 7. The area of the trapezium PQRS in the figure is 18√3 cm² 36√3 cm² 72 cm² 36 cm² 8. A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle? 2√2 2 4√2 √2 9. 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 be 85.5 92.5 87.5 90.5 10. 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 is 60 cm² 20 cm² 40 cm² 30 cm² 11. 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 28/3 cm 7/2 cm 14/3 cm 14 cm 12. 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 7.5 cm, 15 cm 5 cm, 10 cm 2.5 cm, 5 cm 13. There is a vast grassy farm in which there is a rectangular building of the farmhouse whose length and breadth is 50 m and 40 m respectively. A horse is tethered at a corner of the house with a tether of 80 m long. What is the maximum area that the horse can graze? 5425π 254π 5245π 245π 14. 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 (2+√3) r (1+√5) 2r (1+√3) 15. A parallelogram of area 425 cm² has a height of 17cm. The length of the base is 20 cm 50 cm 12.5 cm 25 cm 16. 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 $ 600 $ 86 $ 855 17. 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? 256 37 300 375 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 = √17n h = n h =√13n h= √2n 19. 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, 16 100 m, 15 120 m, 16 20. 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 12 cm 8 cm 5 cm 4 cm 21. All five faces of a regular pyramid with a square base are found to be of the same area. The height of the pyramid is 3 cm. The total area of all its surfaces is 12 sq. cm 15 sq. cm 10 sq. cm 20 sq. cm 22. Find the volume of a closed cylindrical container with radius 5 cm and a height of 34 cm. 450π cubic cm 950π cubic cm 704 cubic cm 850π cubic cm 23. 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. 168 m² 42 m² 22 m² 84 m² 24. 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 5 10/3 20/3 25. 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) 1 out of 25 Time is Up! Time's up