Problems on Volumes and Surface Area

Q21. Find the area of the iron sheet required to prepare a cone 20 cm height with base radius 15 cm.
(a) 1126.60 cm2
(b) 1365.25 cm2
(c) 1750.35 cm2
(d) 1885.71 cm2

Q22. A rectangular water tank is open at the top. Its capacity is 24m3. Its length and breadth are 4 m and 3 m respectively. Ignoring the thickness of the material used for building the tank, the total cost of painting the ineer and outer surfaces of the tank at Rs. 10 per m2 is
(a) Rs. 650
(b) Rs. 750
(c) Rs. 800
(d) Rs. 900

Q23. What will be the area of an iron sheet which can be used to form a cone having base radius 7 cm and height 24 cm ?
(a) 704 cm2
(b) 712 cm2
(c) 726 cm2
(d) 740 cm2

Q24. The ratio of the radius and height of a cone is 5:12. Its volume is 314 2/7 cc. Its slant height is.
(a) 13 cm
(b) 15 cm
(c) 16 cm
(d) 21 cm

Q25. If the ratio of volumes of two cones is 2:3 and the ratio of the raddi of their bases is 1:2, then the ratio of their heights will be
(a) 5:4
(b) 5:3
(c) 7:3
(d) 8:3

Q26. The volume of a hemisphere of radius 7 cm is
(a) 712.5 cm3
(b) 718.6 cm3
(c) 723.6 cm3
(d) 728.3 cm3

Q27. How many balls of diameter 0.4 cm each are formed a cuboid of measuring (4cm X 5cm X 6cm) ?
(a) 3512
(b) 3580
(c) 3620
(d) 3675

Q28. The volume of a sphere is 2145 11/21 cm3. Its diameter is
(a) 16 cm
(b) 18 cm
(c) 21 cm
(d) 23 cm

Q29. A cone of height 15 cm and base diameter 30 cm is carved out of a wooden sphere of radius 15 cm. The percentage of wasted wood is
(a) 61%
(b) 65%
(c) 72%
(d) 75%

Q30. 12 sphere of the same size are made by melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is
(a) 4 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm

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