A) \[\text{83}0\text{ c}{{\text{m}}^{\text{3}}}\]
B) \[\text{38}0\text{ c}{{\text{m}}^{\text{3}}}\]
C) \[\text{3}0\text{8 c}{{\text{m}}^{\text{3}}}\]
D) \[\text{8}0\text{3 c}{{\text{m}}^{\text{3}}}\]
Correct Answer: C
Solution :
Base area of a cylinder \[=\text{38}.\text{5 c}{{\text{m}}^{\text{2}}}\] \[\Rightarrow \] \[\pi {{r}^{2}}=38.5\,c{{m}^{2}}\] \[\Rightarrow \] \[r=\frac{7}{2}cm\] Lateral surface area\[~=\text{176 c}{{\text{m}}^{\text{2}}}\] \[\Rightarrow \]\[2\pi rh=176\,c{{m}^{2}}\Rightarrow h=8\,cm\] \[\therefore \]Volume\[=\pi {{r}^{2}}h=\frac{22}{7}\times {{\left( \frac{7}{2} \right)}^{2}}\times 8\] \[=\text{ 3}0\text{8 c}{{\text{m}}^{\text{3}}}\] Hence, volume of the cylinder\[=\text{ 3}0\text{8 c}{{\text{m}}^{\text{3}}}\]
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