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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?

Speed of the water
= 6 k.m./hr. = 6000 m/hr.
i.e. length of the water column (h) = 6000 m
And, internal radius of the pipe (r)

$equals space 10 space cm. space space space equals space 1 over 10$
$therefore$ Volume if water that flows in 1 hour = $πr squared straight h$

$equals space open parentheses straight pi space cross times space 1 over 10 cross times 1 over 10 cross times 6000 close parentheses straight m cubed equals 60 space straight pi space straight m cubed$
Now, radius of the base of the tank (R)

$equals 10 over 2 space equals space 5 space straight m$

And, Depth of the tank (h = 2m)
$equals space straight pi space straight R squared space straight x space straight H equals space straight pi space straight x space 5 space straight x space 5 space straight x space 2 space equals space 50 space πm cubed$
Hence, Required time to fill the tank by pipe

$fraction numerator Volume space of space the space tank over denominator Volume space of space water space that space flows space in space 1 space hour end fraction equals space space space fraction numerator 50 straight pi over denominator 60 straight pi end fraction equals 5 over 6 hr.$

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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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