Example 6 : A square of side 2 cm. is cut from each corner to form a regular
octagon. What is the side of the octagon? (CAT 2001)
(1) √2/(√2 + 1) (2) √2/(√2 – 1)
(3) 2/(√2 + 1) (4) 2/(√2 – 1)
Example7: A spherical ba
...
Example 6 : A square of side 2 cm. is cut from each corner to form a regular
octagon. What is the side of the octagon? (CAT 2001)
(1) √2/(√2 + 1) (2) √2/(√2 – 1)
(3) 2/(√2 + 1) (4) 2/(√2 – 1)
Example7: A spherical ball of radius 8 cm is cut into 4 equal parts. Total surface area of the parts is:
(1) 384 π cm2 (2) 512 π cm2
(3) 256 π cm2 (4) 488 π cm2
Example8: A cubic meter of silver weighting 900 grams is rolled into a square bar 16 m long. The weight of 1 cm of this bar in grams
is:
(1) 5 grams (2) 5.624 gms.
(3) 0.5625 gms (4) None of the above
Example9: The base of a conical tent is 19.5 m in diameter and the height of the tent is 2.8 m. What area of canvas is required to put
up such a tent?
(1) 300m2 (2) 400 m2
(3) 310.7 m2 (4) none of the above
Example10: The radius of a hemisphere is 7 cm. Find the altitude of a right circular cone of the same base radius and same total
surface area.
(1) 10.38 cm (2) 12.12 cm
(3) 15.66 cm (4) None of the above
Example11: In a rectangular plot 160 m x 120 m, a square tank of side 40 m is dug out a depth of 8 m. The earth so dug out is evenly
spread to cover the remaining area, by how much has the level of plot has been raised?
(1) 0.82 cm (2) 8.2 cm
(3) 0.82 m (4) None of the above
Example12: A cylindrical cistern whose diameter is 21 cm is party filled with water. If a rectangle block of iron measuring 40 cm wholly
immersed in the water, then the rise in the water level (in cm) is:
(1) 13 cm (2) 15.24 cm
(3) 18 cm (4) 19.38 cm
Example13: The corners of an equilateral triangle of side 10cm each are cut to form a regular hexagon. The area of the hexagon is:
(1) 20 cm2 (2) 28.8 cm2
(3) 24.39 cm2 (4) 25.12 cm2
Example14: The surface area of hemisphere is numerically equal to its volume. Its diameter is:
(1) 4.5 units (2) 7.5 units
(3) 9 units (4) 6 units
Example15: Five cylinders of base radius 10 cm and height 1, 2, 3, 4, 5 cm
respectively are melted to form a hemisphere. The surface area of the hemisphere is:
(1) 1615 cm2 (2) 1685 cm2
(3) 1729 cm2 (4) 1836 cm2
Example16: A circular disc of diameter 9 cm is cut in the center and a circular hole is generated. If the weight of the disc is reduced by
one third, then the diameter of the hole is:
(1) 14.3 cm (2) 13.5 cm
(3) 12.4 cm (4) None of the above
Example17: A single pipe of diameter x has to be replaced by six pipes of
diameters 10 cm each. The pipes are used to covey precious liquid in a laboratory. If the speed of the liquid is the same then the value
of x is:
(1) 13cm (2) 18 cm
(3) 24.5 cm (4) 24 cm
Example18: The number of edges of a solid having 20 faces and 32 vertices is:
(1) 58 (2) 56 cm
(3) 50 (4) 59
Example19: The percentage change in the total surface area of a cylinder with volume 1000 c.c. & radius 10 cm when it’s cut into two
equal parts along its cross section is:
(1) 80% (2) 10%
(3) 30% (4) 75.84%
Example 20: Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saves a
distance equal to half the longer side. Then the ratio of the shorter side to the longer side is (CAT 2002)
(1) ½ (2) 2/3
(3) ¼ (4) ¾
Example21: Water flows through a pipe of diameter 1/16 meter, at 6 meters/sec. The time taken to fill bath 2 metres by 3 meters by 4
meters is:
(1) 21.8 min (2) 30.33 min
(3) 15.38 min (4) None of these
Example22: A tank 72 cm long, 60 cm wide, 36 cm high contains water to a depth of 18 cm. A metal bloc 48 cm by 36 cm by 15 cm is
put into the tank and totally submerged. The rise of water- level is:
(1) 5 cm (2) 5.27 cm(3) 6.36 cm (4) 6 cm
Example23: The external diameter of a hollow metal sphere is 14 cm and its thickness is 2 cm. Find the radius of a solid sphere
containing the same amount of material as the hollow sphere.
(1) 6 cm (2) 5 cm
(3) 4 cm (4) 4.5 cm
Example24: Three solid metal of radii 3 cm, 4 cm, 5 cm respectively, are melted
together. The metal is recast as a single solid sphere. The percentage reduction in the area of surface resulting from this is:
(1) 40% (2) 16%
(3) 12% (4) 28%
Example25: A bucket in the form of a frustum of a right circular cone is 48 cm deep and the radii of the top and bottom are 20 cm and
16 cm respectively. The volume of water it will hold is:
(1) 49049 c.c. (2) 30000 c.c.
(3) 31259 c.c. (4) 24076 c.c.
Example 26: The diameter of a copper sphere is 6 cm. The sphere is melted and is drawn into a long wire of uniform circular cross
section. If the length of the wire is 36 cm, The radius is
(1) 1 (2) 0.5
(3) 2 (4) 0.1
Example 27 : A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel, party filled with water. The diameter of the
cylindrical vessel is 12cm. If the sphere is completely-submerged in water, by how much will the level of water rise in the cylindrical
vessel?
(1) 2 (2) 0.5
(3) 1 (4) 0.1
Example 28: In the given figure AB and BC are 24 and 32 with included angle of 90o. The other sides are 25 each and none of the
other angle is 90o. Find the area of the fig. (CAT 2001)
(1) 684 (2) 786
(3) 880 (4) None of these.
Example 29 : Find the number of coins, 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10
cm and diameter 4.5 cm.
(1) 425 (2) 450
(3) 550 (4) None of these.
Example 30: A solid iron rectangular block of dimensions 4.4 m, 2.6m and 1 m is
cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.
(1) 118 (2) 116
(3) 110 (4) 112
Example31: How many sides have regular polygon whose exterior angle is 1/11 of its interior angle?
(1) 22 (2) 24
(3) 20 (4) 26
Example32: The angles of a pentagon are xo, x + 20o, x + 40o, x + 60o and
x + 80o. The smallest angle of the pentagon is:
(1) 65o (2) 70o
(3) 68o (4) 60o
Example33: In a triangle ABC, the altitudes BD and CE are equal and ∠A = 36o. What is the value of the angle B?
(1) 65o (2) 60o
(3) 75o (4) 72o
Example 34: In the following figure
AE = EF = FB. The ratio of area of triangle CEF and rectangle ABCD is (CAT 2001)
(1) 1/6 (2) 1/8
(3) 1/9 (4) None of these.
Example35: The interior angle of a regular polygon exceeds the exterior angle by 140o. The sides of the polygon are:
(1) 18 (2) 22
(3) 25 (4) 15
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