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Surface Areas and Volumes

Short Answer Type

501. A spherical ball of lead 3 cm in diameter, is melted and recast into three spherical balls. The diameters of two of these balls are 1 cm and 1.5 cm. Find the diameter of the third ball.

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502. The radius and height of a cylinder are 8 cm and 64 cm respectively, it is recast into a sphere whose volume is

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of the volume of the cylinder. Find the radius of the sphere.

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503. A right circular cone is 4.6 cm high and the radius of its base is 1.4 cm it is melted and recast into a right circular cone with radius 2.1 cm. Find its height.

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504. The diameter of a metallic sphere is equal to 9 cm it is melted and drawn into a long wire of diameter 2 mm having uniform cross section. Find the length of the wire.

Solution not provided.

Ans. 12150 cm

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505. A metallic sphere of diameter 3 cm is melted and recast into three spheres. The radius of one of these sphere is 0.75 cm and that of another is 1.25 cm. Determine the radius of the third sphere.

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506. A well, whose diameter is 7 m, has been dug 22.5 m deep and the earth dug out is used to form an embankment 10.5 m wide around it. Find the height of the embankment.

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507. A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment.

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508. A well of diameter 8 m is dug 14 m deep. The earth taken out of it is spread evently all around a width of 3m to form an embankment. Find the height of the embankment.

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509. An agricultural field is in the form of rectangle of length 22 m and width 14 m. A 20 m deep well of diameter 14 m is dug in a corner of the field and earth taken out of the well is spread evenly over the remaining part of the field. Find the rise in the level.

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510. A solid sphere of radius r is melted and recast into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm. Its height 24 cm and thickness 2 cm, find the radius r.

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