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 cm
2
(2) 512 π cm
2
(3) 256 π cm
2
(4) 488 π cm
2
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) 300m
2
(2) 400 m
2
(3) 310.7 m
2
(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 cm
2
(2) 28.8 cm
2
(3) 24.39 cm
2
(4) 25.12 cm
2
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 cm
2
(2) 1685 cm
2
(3) 1729 cm
2
(4) 1836 cm
2
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
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 Summer '09
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