Today is DAY 24 of the study plan and in Quantitative Aptitude today’s chapter is Mensuration – Volume
Q1. A 3.3 m high room is half as long again as it is wide and its volume is 123 (3/4) m^3. Find out its length and breadth.
(a) 7.5 m, 6 m
(b) 8 m, 5 m
(c) 7.5 m, 5 m
(d) 8.5 m, 5 m
(e) None of these
Q2. 2 cubes have volumes in the ratio 1:27. The ratio of the area of the face of one to that of the other is:
(a) 1 : 2
(b) 1 : 3
(c) 1 : 6
(d) 1 : 9
(e) None of these
Q3. A cube of edge 3 cm of iron weighs 12 gm. What is the weight of a similar cube of iron whose edge is 12 cm?
(a) 768 gm
(b) 678 gm
(c) 964 gm
(d) 864 gm
(e) None of these
Q4. A cylindrical jar of diameter 24 cm contains water to a height of 30 cm. A spherical steel ball is dropped into the jar and the level of the water rises by 67.5 mm. The diameter of the ball is:
(a) 16 cm
(b) 15 cm
(c) 20 cm
(d) 18 cm
(e) None of these
Q5. If the radius of a sphere is doubled, then its volume is increased by:
(a) 100%
(b) 200%
(c) 700%
(d) 800%
(e) None of these
Q6. A ball of lead, 4 cm in diameter, is covered with gold. If the volume of the gold and lead are equal, then the thickness of gold is approximately [given∛2=1.259]
(a) 5.038 cm
(b) 5.190 cm
(c) 1.038 cm
(d) 0.518 cm
(e) None of these
Q7. A conical cup is filled with ice cream. The ice cream forms a hemispherical shape on its open top. The height of the hemispherical part is 7 cm. The radius of the hemispherical part equals the height of the cone. Then the volume of the ice cream is [π=22/7]
(a) 1078 m^3
(b) 1708 m^3
(c) 7108 m^3
(d) 7180 m^3
(e) None of these
Q8. Assume that a drop of water is spherical and its diameter is 1/10 of a centimeter. A conical glass has a height equal to the diameter of its rim. If 32,000 drops of water fill the glass completely, then the height of the glass (in cm) is:
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of these
Q9. A rectangular block of metal has dimensions 21 cm, 77 cm and 24 cm. The block has been melted into a sphere. The radius of the sphere is (Take π=22/7)
(a) 21 cm
(b) 7 cm
(c) 14 cm
(d) 28 cm
(e) None of these
Q10. A field is in the form of a rectangle of length 18 m and width 15 m. A pit, 7.5 m long, 6 m broad and 0.8 m deep, is dug in a corner of the field and the earth taken out is evenly spread over the remaining area of the field. The level of the field raised is:
(a) 12 cm
(b) 14 cm
(c) 16 cm
(d) 18 cm
(e) None of these
Q11. A cylindrical can whose base horizontal and is of internal radius 3.5 cm contains sufficient water so that when a solid sphere is placed inside, water just covers the sphere. The sphere fits in the can exactly. The depth of water in the can before the sphere was put is:
(a) 35/3 cm
(b) 17/3 cm
(c) 7/3 cm
(d) 14/3 cm
(e) None of these
Q12. The height of a right prism with a square base is 15 cm. If the area of the total surfaces of the prism is 608 cm^2, its volume is:
(a) 910 cm^2
(b) 920 cm^2
(c) 960 cm^2
(d) 980 cm^2
(e) None of these
Q13. The height of a right circular cone and the radius of its circular base are 9 cm and 3 cm respectively. The cone is cut by a plane parallel to its base so as to divide it into two parts. The volume of the frustum (i.e., the lower part) of the cone is 44 cm^3. The radius of the upper circular surface of the frustum (taking π=22/7) is:
(a) ∛12 cm
(b) ∛13 cm
(c) ∛6 cm
(d) ∛20 cm
(e) None of these
Q14. The number of coins, each of radius 0.75 cm and thickness 0.2 cm, to be melted to make a right circular cylinder of height 8 cm and radius 3 cm, is:
(a) 640
(b) 600
(c) 500
(d) 480
(e) None of these
Q15. 3 spherical balls of radii 1 cm, 2 cm and 3 cm are melted to form a single spherical ball. In the process, the loss of material is 25%. The radius of the new ball is:
(a) 6 cm
(b) 5 cm
(c) 3 cm
(d) 2 cm
(e) None of these