A cylinder vessel of diameter 14cm and height 42cm is fixed symmetrically inside a similar vessel of diameter 16cm and height 42cm. The total space between the two vessels is filled with cork dust for heat insulation purposes. The number of cubic centimeters of cork dust will be required is

# A cylinder vessel of diameter 14cm and height 42cm is fixed symmetrically inside a similar vessel of diameter 16cm and height 42cm. The total space between the two vessels is filled with cork dust for heat insulation purposes. The number of cubic centimeters of cork dust will be required is

1. A
$1990{\text{cm}}^{3}$
2. B
$1980{\text{cm}}^{3}$
3. C
$1982{\text{cm}}^{3}$
4. D
$1984{\text{cm}}^{3}$

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### Solution:

Radius of inner cylindrical vessel $=7$

Radius of outer cylindrical vessel $=8$

Height both inner and outer cylindrical vessel $=42$

The total space between the two vessels is filled with cork dust for heat insulation $=$ Volume of outer cylindrical vessel $-$ Volume of inner cylindrical vessel

$=\frac{22}{7}×8×8×42-\frac{22}{7}×7×7×42$

$=\frac{22}{7}×42\left(64-49\right)$

$=\frac{22}{7}×42×15$

$=1980{\text{cm}}^{3}$

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