The rain water from a roof 22 m × 20 m drains into a cylindrical vessel having a diameter of 2 m and height 3.5 m. If the vessel is just full, then the rainfall (in cm) is:
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Aptitude · all questionsMensuration 3d
Mensuration 3d
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The base of a right prism is an equilateral triangle. If the lateral surface area and volume are 120 cm2, 40√3 cm3 respectively then the side of base of the prism is
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A solid cube is cut into three cuboids of same volumes. What is the ratio of the surface area of the cube to the sum of the surface areas of any two of the cuboids so formed?
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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 (given = 1.259) is approximately
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A right triangle with sides 9 cm, 12 cm and 15 cm is rotated about the side of 9 cm to form a cone. The volume of the cone so formed is:
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The volume of a right circular cone is 1232 cm3 and its vertical height is 24 cm. Its curved surface area is
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The curved surface area of a cylinder is five time the area of its base. Find the ratio of radius and height of the cylinder.
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A hollow cylindrical tube 20 cm long is made of iron and its external and internal diameters are 8 cm and 6 cm respectively. The volume of iron used in making the tube is
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A solid cone of height 9 cm with diameter of its base 18 cm is cut out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is:
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If the number of vertices, edges and faces of a rectangular parallelopiped are denoted by v, e and f respectively, the value of (v - e + f) is
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The curved surface area and volume of a cylindrical object are 88 cm2 and 132 cm3, respectively. The height (in cm) of the cylindrical object is:
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The ratio of weights of two spheres of different materials is 8 : 17 and the ratio of weights per 1 cc of materials of each is 289 : 64. The ratio of radii of the two spheres is
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The base of a right prism is a trapezium. The length of the parallel sides are 8 cm and 14 cm and the distance between the parallel sides is 8 cm. If the volume of the prism is 1056 cm3, then the height of the prism is
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Determine the total surface area of a hemisphere closed at bottom. Radius of the hemisphere is unit.
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A cylindrical tube, open at both ends, is made of a metal sheet which is 0.5 cm thick. Its outer radius is 4 cm and length is 2 m. How much metal (in cm3) has been used in making the tube?
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If the height of a cylinder is 4 times its circumference, the volume of the cylinder in terms of its circumference, is
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The areas of three consecutive faces of a cuboid are 12 cm2, then the volume (in cm3) of the cuboid is
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The ratio of the height and the diameter of a right circular cone is 6 : 5 and its volume is What is its slant height?
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A sphere of maximum volume is cut out from a solid hemisphere. What is the ratio of the volume of the sphere to that of the remaining solid?
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A cube of edge 6 cm is painted on all sides and then cut into unit cubes. The number of unit cubes with no sides painted is
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