If the volume of a cylindrical pillar is 924 m\(^3\) and its curved surface area is 264 m\(^2\)then the total surface area is __________.
If the volume of a cylindrical pillar is 924 m\(^3\) and its curved surface area is 264 m\(^2\)then the total surface area is __________.
यदि एक बेलनाकार स्तंभ का आयतन 924 m\(^3\) है और इसका वक्र पृष्ठीय क्षेत्रफल 264 m\(^2\) है, तो कुल पृष्ठीय क्षेत्रफल __________है।
Detailed Solution & Logic
182 \(\pi\text{m}^2\)
Given:
Volume $= \pi r^2 h = 924$
Curved surface area $= 2\pi r h = 264$
Divide:
$\frac{\pi r^2 h}{2\pi r h} = \frac{924}{264} \Rightarrow \frac{r}{2} = 3.5 \Rightarrow r = 7$
Now,
$2\pi r h = 264 \Rightarrow 2\pi \cdot 7 \cdot h = 264 \Rightarrow 14\pi h = 264$
Using $\pi = \frac{22}{7}$:
$44h = 264 \Rightarrow h = 6$
Total surface area:
$2\pi r (r + h) = 2\pi \cdot 7 (7 + 6) = 14\pi \cdot 13 = 182\pi$
So, the correct answer is 182 $\pi \text{ m}^2$.
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