A) \[\text{325 c}{{\text{m}}^{\text{3}}}\]
B) \[\text{328 c}{{\text{m}}^{\text{3}}}\]
C) \[\text{33}0\text{ c}{{\text{m}}^{\text{3}}}\]
D) \[\text{332 c}{{\text{m}}^{\text{3}}}\]
Correct Answer: D
Solution :
Height of cone \[=15\text{ }cm,\]Radius of cone \[=6\text{ m}\] \[\therefore \]Volume of cone \[=\frac{1}{3}\pi \,\,{{r}^{2}}h\] \[=\frac{1}{3}\times \frac{22}{7}\times 6\times 6\times 15\] \[=\frac{3960}{7}\,cu.\,cm.\] \[=565.71\,cu.\,cm\] Now base of the pyramid is an equilateral triangle of side \[6\text{ }cm\] \[\therefore \] Area of equilateral triangle \[=\frac{\sqrt{3}}{4}\times {{(6\sqrt{3})}^{2}}=27\sqrt{3}\] \[\therefore \] Volume of pyramid of height \[15\text{ }cm\] \[=\frac{1}{3}\times 27\sqrt{3}\times 15\] \[=135\sqrt{3}\] \[=233.82\] Hence, difference of volume of cone and pyramid \[=(565.71-233.82\] \[=332\,cu.\,cm\,\,(app.)\]
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