Aptitude · all questions

Volume And Surface Area
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Q141

If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, then the diameter of the new sphere will be :

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Q142

A rectangular tank measuring 5 m × 4.5 m × 2.1 m is dug in the centre of the field measuring 13.5 m by 2.5 m. The earth dug out is evenly spread over the remaining portion of the field. How much is the level of the field raised ?

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Q143

If the areas of three adjacent faces of a cuboid are x, y, z respectively, then the volume of the cuboid is :

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Q144

How many cubes of 10 cm edge can put in a cubical box of 1 m edge ?

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Q145

Two rectangular sheets of paper, each 30 cm × 18 cm are made into two right circular cylinders, one by rolling the paper along its length and the other along the breadth. The ratio of the volumes of the two cylinders, thus formed, is :

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Q146

Diameter of a jar cylindrical in shape is increased by 25%. By what percent must the height be decreased so that there is no change in its volume :

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Q147

Water is flowing at the rate of 5 km/hr through a cylindrical pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Determine the time in which the level of water in the tank will rise by 7 cm :

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Q148

Water flows at the rate of 10 metres per minutes from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm ?

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Q149

If the radius of a sphere is doubled, how many times does its volume becomes ?

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Q150

The volume of two spheres are in the ratio of 64 : 27. The ratio p their surface areas is :

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Q151

A right circular cylinder and a sphere are of equal volumes and their radii are also equal. If h is the height of the cylinder and d, the diameter of the sphere, then :

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Q152

A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is :

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Q153

A plot of land in the form of a rectangle has dimensions 240 m × 180 m. A drain-let 10 m wide is dug all around it (outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. The depth of the drain-let is :

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Q154

If the areas of three adjacent faces of a rectangular block are in the ratio of 2 : 3 : 4 and its volume is 9000 cu.cm; then the length of the shortest side is :

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Q155

A 4 cm cube is cut into 1 cm cubes. The total surface area of all the small cubes is :

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Q156

A well has to be dug out that is to be 22.5 m deep and of diameter 7 m. Find the cost of plastering the inner curved surface at Rs. 3 per sq.meter :

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Q157

A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by :

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Q158

The truck of a tree is a right cylinder 1.5 m in radius and 10 m high. The volume of the timber which remains when the truck is trimmed just enough to reduce it to a rectangular parallelopiped on a square base is :

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Q159

The radius and height of a right circular cone are in the ratio 3 : 4. If its volume is

301 \frac{5}{7}

cm³, what is its slant height ?

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Q160

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. The area of the canvas required for the tent is :

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