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.

A Square ABCD, of Side 4 Cm

40. Find the area of the shaded region, which contains two semi-circles, and a rectangle of breadth 1 cm.

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.

A Metallic Cylinder Has a Radius 3 Cm and Height 5 Cm

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.

A Pen Stand Made of Wood

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:

The Median of the Following Data is 525. Find the Values of X and Y if the Total Frequency is 100
Classes0 - 100100 - 200200 - 300300 - 400400 - 500500 - 600600 - 700700 - 800800 - 900900 - 1000

50. During the medical checkup of 35 students of a class, their weights were recorded as follows

During the Medical Checkup of 35 Students of a Class, Their Weights Were Recorded as Follows
Weight (in kg)Number of students
Less than 380
Less than 493
Less than 435
Less than 449
Less than 4514
Less than 4828
Less than 5032
Less than 5235

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.