Volume and Surface Area
Quantitative Aptitude
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Quantitative Aptitude • Volume and Surface Area
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A sphere of radius 5 cm is placed inside a right circular cylinder such that it touches both the base and curved surface. What is the ratio of the volume of the sphere to the volume of the cylinder?
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Quantitative Aptitude • Volume and Surface Area
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A right circular cone is cut by a plane parallel to its base into two parts. The ratio of the volumes of the smaller cone and the frustum is 1:7. What is the ratio of the height of the smaller cone to the height of the original cone?
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Quantitative Aptitude • Volume and Surface Area
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A rectangular parallelopiped has dimensions in the ratio 3:4:5. If its total surface area is 846 cm², what is the length of its diagonal?
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Quantitative Aptitude • Volume and Surface Area
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A cube of side 12 cm is painted on all faces and then cut into smaller cubes of side 2 cm each. How many of the smaller cubes have exactly one face painted?
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Quantitative Aptitude • Volume and Surface Area
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The total surface area of a cube is equal to the surface area of a sphere. What is the ratio of the volume of the cube to the volume of the sphere?
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Quantitative Aptitude • Volume and Surface Area
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A solid metallic hemisphere of radius 8 cm is melted and recast into a right circular cone of base radius 6 cm. What is the height of the cone?
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Quantitative Aptitude • Volume and Surface Area
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A right circular cone of height 24 cm and base radius 6 cm is cut by a plane parallel to its base into a smaller cone and a frustum. If the height of the smaller cone is 6 cm, what is the ratio of the volume of the frustum to the volume of the original cone?
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Quantitative Aptitude • Volume and Surface Area
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A solid consists of a cylinder with a hemisphere on top and a cone at the bottom, all having the same radius of 7 cm. If the height of the cylinder is 10 cm and the height of the cone is 24 cm, what is the total volume of the solid?
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Quantitative Aptitude • Volume and Surface Area
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A cylindrical vessel of radius 6 cm contains water up to a height of 10 cm. A solid sphere of radius 3 cm is completely immersed in the water. What is the rise in water level?
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Quantitative Aptitude • Volume and Surface Area
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A metallic wire of diameter 2 mm is evenly wound around a cylinder of radius 7 cm and height 20 cm to cover its curved surface completely. What is the length of the wire?
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