NCERT Class 10 Mathematics Higher Order Thinking Skills CBSE Board Sample Problems Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)
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39. In the given figure, from each comer of a square ABCD, of side 4 cm, quadrant of a circle of radius 1 cm each is cut and a circle of radius 1 cm is cut from the centre. Find the area of the shaded region.
40. Find the area of the shaded region, which contains two semi-circles, and a rectangle of breadth 1 cm.
41. A metallic cylinder has a radius 3 cm and height 5 cm. It is made of metal A. To reduce its weight a conical hole is drilled in the cylinder (as shown in the figure) and it is completely filled with a lighter metal B. The conical hole has a radius of cm and ts depth is cm. Calculate the ratio of the volume of the metal A to the volume of metal 13 in the solid.
42. Two sphere of the same metal weigh 1 kg and 7 kg. The radius of the smaller sphere is 3 cm. The two spheres are melted to form a single big sphere. Find the diameter o ′ the bigger sphere.
43. A spherical copper shell of external diameter 18 cm is melted and recast into a solid cone f base radius 14 cm and height cm. Find the inner diameter of the shell.
44. A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are . The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm.
Find the volume of wood in the entire stand.
45. A vessel is in the form of an inverted cone. Its height is 8cm and radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one fourth of the water flows out. Find the number of lead shots dropped.
46. A container, shaped like a circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled in cones of height 6 cm and diameter 3 c i having a hemispherical shape on the top of the same radius of base as that of cone. Find the number of such cones that can be filled with ice cream.
47. A container open at the top and made of metal sheet, is in the form of a frustum of a cone of eight 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk, which can completely fill the container, at the rate of ₹ 20 per litre. Also, find the cost of metal sheet used to make the container, if t costs ₹ 8 per (Use )
48. A metallic right circular cone 20 cm high and whose vertical angle is is cut into two parts at the middle of its height by a plane parallel to the base. If the frustum so obtained is melted and drawn into a wire of diameter 1 cm, find the length of the wire.
49. The median of the following data is 525. Find the values of x and y if the total frequency is 100:
| Classes | 0 - 100 | 100 - 200 | 200 - 300 | 300 - 400 | 400 - 500 | 500 - 600 | 600 - 700 | 700 - 800 | 800 - 900 | 900 - 1000 |
| Frequency | 2 | 5 | X | 12 | 17 | 20 | Y | 9 | 7 | 4 |
50. During the medical checkup of 35 students of a class, their weights were recorded as follows
| Weight (in kg) | Number of students |
| Less than 38 | 0 |
| Less than 49 | 3 |
| Less than 43 | 5 |
| Less than 44 | 9 |
| Less than 45 | 14 |
| Less than 48 | 28 |
| Less than 50 | 32 |
| Less than 52 | 35 |
Draw a less than type ogive for the above data. Hence, obtain the median weight from the graph and verify the result by using the formula.