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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