Welcome to your Mensuration(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. The angle of a sector of a circle of radius 4.2 cm is 150°.If π = 22/7, the perimeter of the sector is15.2 cm19.4 cm11 cm16.8 cm2. In the triangle PQR shown 108 cm²144 cm²72 cm²36 cm²3. 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 are10 cm, 20 cm2.5 cm, 5 cm5 cm, 10 cm7.5 cm, 15 cm4. 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.120π/380π/3100π/3110π/35. 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.28 cm14 cm20 cm15 cm6. 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 is15 sq. cm10 sq. cm20 sq. cm12 sq. cm7. 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?2.53.83.548. Find the total surface area of a closed cylindrical container with radius 5 cm and a height of 34 cm.220π sq. cm130π sq. cm320π sq. cm390π sq. cm9. 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 (1+√3)2r+√3r (1+√5)2r (2+√3)10. 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?234111. 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? 1/121/61/241/1812. 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 be87.590.585.592.513. 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 is40 cm²20 cm²60 cm²30 cm²14. A square tile measures 20 cm by 20 cm. How many of such tiles will cover a floor measuring 5m by 4m40025050032015. Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is475616. ABCDEF is a regular hexagon of side 6 cm. What is the area of triangle BDF?24 cm²27√3 cm²22 cm²32√3 cm²17. 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.What is the area of the region PQRST enclosed by the figure, to the nearest whole number48 cm²24 cm²96 cm²193 cm²18. 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 is864 cm31500 cm3540 cm3900 cm319. 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 tan 30°) cm(5 sin 30°) cm20. Find the area of the shaded region in the given figure of square ABCD128 cm²148 cm²128 cm²192 cm²21. 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 cm3.5 cm10.5 cm7.0 cm22. 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 is8,552 cm312,000 cm39,888 cm38,224 cm323. In the diagram, O is the center with radius 7 cm and <QPR = 30°. Find the length of arc QR (Take π = 22/7) 12 cm21/2 cm22/3 cm11/3 cm24. 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/n² cmh/√n cmh/n cmn/h² cm25. 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 is75:1645:45:3625:4826 out of 25Time is Up! Time's up
