Untitled

1. A statue 1.6 m tall, stands on the top of a pedestal.
From a point on the ground, the angle of elevation of the

top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the
height of the pedestal. (use √ 3 = 1.73 ) (2.184 m)
2. A small terrace at a hockey ground comprises of 10 steps each of which 20 m long and built of solid concrete.
Each step has a rise of 1/4 m and a tread of 1/2 m. Calculate the total volume of concrete required to build the
terrace. (137.5 m3)
3. A tightly stretched rope of length 20 m is tied from the top of a vertical pole to the ground. Find the height of
the pole, if the angle made by the rope is 30 0 . (10m)
4. From the top of a 7 m high building the angle of elevation of the top of a tower is 60° and the angle of
depression of its foot is 45°. Determine the height of the tower. (7( √ 3 + 1)m
5. Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface
area of the shape so formed. ( 855 cm2 approx.)
6. An iron pole consists of a cylinder of height 240 cm and base diameter 26 cm, which is surmounted by another
cylinder of height 66 cm and radius 10 cm. Find the mass of the pole given that 1 cm3 of iron has approximately
8 g mass. [take, π = 3.14] ( 1184.66 kg)
7. If a pole 6 m high casts a shadow 2√ 3 m long on the ground, then find the Sun’s elevation. ( 60 0 )
8. The length of a string between a kite and a point on the ground is 85 m. If the string makes an angle θ with the
ground level such that tan θ = 15/ 8 , then find the height of kite. (75 m)
9. The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 0.5 cm in diameter. A full barrel of ink in the
pen can be used for writing 275 words on an average. How many words would be written using a bottle of ink
containing one-fourth of a litre? (5000)
10. 500 persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water
level in the pond, if the average displacement of the water by a person is 0.04 m 3 ? (0 5. Cm)
11. A wall 24 m long, 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm × 16 cm × 10
cm. If the mortar occupies 1/10 th of the volume of the wall, then find the number of bricks used in
constructing the wall. (12960)
12. If the height of a tower and the distance of the point of observation from its foot, both are increased by 10%,
then the angle of elevation of its top remains unchanged. Explain
13. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the
cylinder is 10 cm and its base is of radius 3.5 cm. Find the total surface area of the article. (594 cm 2 )
14. There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are points
directly opposite to each other on two banks and in line with the tree. If the angles of elevation of the top of
the tree from P and Q are respectively 30° and 45°, then find the height of the tree. (use √ 3 = 1.732] (36 6. M)
15. A man standing on the deck of a ship, which is 10 m above the water level. He observes that the angle of
elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. Calculate the
distance of the hill from the ship and height of the hill. (10 √ 3 , 40m)
16. A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle of elevation
50
from 600 to 450 . Find the speed of the boat. ( ( 3−√3 )m/min
3
17. A girl 8 m tall spots a parrot sitting on the top of a building of height 58 m from the ground. The angle of
elevation of the parrot from the eyes of girl at any instant is 60°. The parrot flies away horizontally in such a way
that it remained at a constant height from the ground. After 8 s, the angle of elevation of the parrot from the
same point is 30°. Based on the above information, answer the following questions. (use √ 3 = 1.732]
10 0
(i) Find the distance of first position of the parrot from the eyes of the girl. ( m)
√3
(ii) If the distance between the position of parrot increases, then the angle of elevation decreases. Justify with girl
50
(iii) Find the distance between the girl and the building. ( m)
√3
(iv) The distance covered by the parrot. (57.50 m)
(v) Find the speed of the parrot in 8 s. ( 7.225 m/s)
18. A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 8 m of uniform thickness. Find the
thickness of the wire. ( 1/10 cm)
19. A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast
into the form of a cone of base diameter 8 cm. Find the height of the cone. (14 cm)
20. A well of diameter 10 m is dug 14 m deep. The Earth taken out of it is spread evenly all around to a width of 5 m
to form an embankment. Find the height of embankment. (4 67. M)
21. If a hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that
1/8 space of the cube remains unfilled. Then, find the number of marbles that the cube can be accommodated.
(142244 (approx.)
22. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 3 cm
and the diameter of the base is 4cm. Determine the volume of the solid toy. If a right circular cylinder
circumscribes the toy, then find the difference of the volumes of the cylinder and the toy. [take, π = 3 14 (33.49
cm 3)

Untitled

Uploaded by

Copyright:

Available Formats

Untitled

Uploaded by

Document Information

Original Description:

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Untitled

Uploaded by

Copyright:

Available Formats

1. A statue 1.6 m tall, stands on the top of a pedestal.

From a point on the ground, the angle of elevation of the

You might also like