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Mathematics : Surface Areas and Volumes

Short Answer Type

491. A spherical copper shell, of external diameter 18 cm, is melted and recast into a solid cone of base radius 14 cm and height

4 3 over 7 space cm.

Find the inner diameter of the shell.

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492. A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 6km/h, in how much time will the tank be filled?

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493. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have ? Find the surface area of the solid.

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494. Three cubes each of side 5 cm are joined end to end. Find the surface area of the resulting cuboid.

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495. Two cubes each of volume 64 m³ are joined end to end. Find the surface area and volume of the resulting cuboid.

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496. Three cubes of side 6 cm are joined end to end. Find the surface area of the resulting cuboid.

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497. A piece of metal in the form of a cone of diameter 2 cm and height 9 cm is melted and recast into a cylinder of radius 1 cm. Find the height of the cylinder.

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498.

A cone 8.4 cm high and the radius of its base is 2.1 cm it is melted and recast into a sphere. Find the radius of the sphere.

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499. A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

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500. A metallic sphere of, radius 8 cm is melted into three spheres. Radii of two spheres are 6 cm and 4 cm. Find the radius of the third sphere.

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