Mathematics - Class X Question Paper - Central Board Of Secondary Education Page 7
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33SECTION C
Q21. Prove that the angle subtended by an arc of a circle at its center is double the angle
subtended by it at any point on the remaining part of the circle.
Using the above result prove that the angle in a major segment is acute.
Q22. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the
squares of their corresponding sides.
Using the above, prove that the area of an equilateral triangle described on the side of
a square is half the area of the equilateral triangle described on its diagonal.
Q23. From the top of a tower 60m. high, the angles of depression of the top and bottom of a
building whose base is in the same straight line with the base of the tower are observed
to be 30° and 60° respectively. Find the height of the building.
OR
An aeroplane flying horizontally at a height of 1.5km above the ground is observed at
a certain point on earth to subtend an angle of 60°. After 15 seconds, its angle of elevation
at the same point is observed to be 30°. Calculate the speed of the aeroplane in km/h.
Q24. A solid toy is in the form of a hemisphere surmounted by a right circular cone. If the
height of the cone is 4 cm and diameter of the base is 6 cm calculate :
i) the volume of the toy
ii) surface area of the toy (use π = 3.14)
OR
A bucket of height 8cm. and made up of copper sheet is in the form of frustrum of a
right circular cone with radii of its lower and upper ends as 3 cm and 9 cm respectively.
Calculate :
i) the height of the cone of which the bucket is a part
ii) the volume of water which can be filled in the bucket.
iii) the area of copper sheet required to make the bucket (Leave the answer in
terms of π)
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