Question : The radius and height of a cylinder are in the ratio 4: 7 and its volume is 2816 cm3. Find its radius. (Take $\pi=\frac{22}{7}$ )
Option 1: 5 cm
Option 2: 7 cm
Option 3: 8 cm
Option 4: 6 cm
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Correct Answer: 8 cm
Solution :
The ratio of the radius and the height = 4 : 7
Volume of a cylinder = 2816 cm$^3$
Volume of a cylinder = $\pi × r^2 × h$
Let the radius and the height of a cylinder be $4x$ and $7x$ respectively.
⇒ $\frac{22}{7} × (4x)^2 × 7x$ = 2816
⇒ $16x^2 × 7x = \frac{(2816 × 7)}{22}$
⇒ $(16 × 7)x^3 = 128 × 7$
⇒ $x^3 = \frac{(128 × 7)}{(16 × 7)}$
⇒ $x^3 = 8$
⇒ $x = 2$
Radius = 4 × 2 = 8 cm
$\therefore$ The radius of a cylinder is 8 cm.
Hence, the correct answer is 8 cm.
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