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A spherical vessel of diameter14 cm and height42cm is fixed symmetrically inside a similar vessel of diameter16cm and height42cm. The total space between the two vessels is filled with cork dust for heat insulation purposes. How many cubic centimeters of cork dust will be required?

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1980 {cm}^{3}

2084 {cm}^{3}

3571 {cm}^{3}

4175 {cm}^{3}

answer is A.

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Detailed Solution

Given,
Inner diameter = 16 cm, So,
Inner radius

r_{1} = \frac{16}{2} = 8 cm

Outer diameter = 14 cm, So,
Inner radius

r_{2} = \frac{14}{2} = 7 cm

Now height= 42 cm
The volume of cork dust is equal to the difference of the inner and outer cylinder volumes.
Thus, required volume,

V = π r_{2}^{2} h - π r_{1}^{2} h

V = π (r_{2}^{2} - r_{1}^{2}) h

V = π (8^{2} - 7^{2}) 42

V = 1980 {cm}^{3}

The volume of cork dust will be

1980 {cm}^{3}

Correct option is 1.

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