Question

Curved surface area of cylinder is 264m square and volume is 964 cm 3 cube. Find the ratio of height to its diameter.
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Answer 1

Correct Question :

›»› Curved surface area of cylinder is 264m square and volume is 964 m³. Find the ratio of height to its diameter.

Answer :

›»› The ratio of height to its diameter is 3:7.

Given :

• Curved surface area of cylinder is 264 m² and volume is 964 m³.

To Find :

• The ratio of height to its diameter.

Solution :

Let us assume that, the radius of a cylinder is r m and height of a cylinder is h m respectively.

As it is given that the curved surface area of cylinder is 264 m².

→ 2πrh = 264 m² ......(❶)

As it is also given that the volume of cylinder is 964 m³.

→ πr²h = 964 m³ ......(❷)

Now, let us divide equation (❷) by equation (❶).

$\tt{:\implies \dfrac{\pi{r}^{2}h }{2\pi rh} = \dfrac{924}{264} }$

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$\tt{:\implies \dfrac{\pi \times {r}^{2} \times h}{2 \times \pi \times r \times h} = \dfrac{924}{264} }$

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$\tt{:\implies \dfrac{ \not{\pi} \times \not{r} \times r\times \not{h}}{2 \times \not{\pi} \times \not{r} \times \not{h}} = \dfrac{924}{264} }$

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$\tt{:\implies \dfrac{r}{2 } = \dfrac{ \cancel{924}}{ \cancel{264}} }$

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$\tt{:\implies \dfrac{r}{2 } = \dfrac{7}{2} }$

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$\bf{:\implies r = 7}$

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$\tt{:\implies \mathscr{D}iameter = 2r}$

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$\tt{:\implies \mathscr{D}iameter = 2 \times 7}$

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$\bf{:\implies \mathscr{D}iameter = 14}$

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From equation (❶),

$\tt{:\implies 2\pi rh = 264}$

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$\tt{:\implies \not{2} \times \dfrac{22}{7} \times \dfrac{14}{ \not{2}} \times h = 264}$

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$\tt{:\implies \dfrac{22}{ \cancel{7}} \times \cancel{14} \times h = 264}$

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$\tt{:\implies 22 \times 2 \times h = 264}$

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$\tt{:\implies 44 \times h = 264}$

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$\tt{:\implies 44h = 264}$

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$\tt{:\implies h = \cancel{\dfrac{264}{44}} }$

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$\bf{:\implies h = 6}$

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Now,

$\tt{:\implies \mathscr{R}atio = \dfrac{ \mathscr{H}eight}{ \mathscr{D}iameter}}$

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$\tt{:\implies \mathscr{R}atio = \cancel{\dfrac{6}{14}}}$

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$\tt{:\implies \mathscr{R}atio = \dfrac{3}{7} }$

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$\bf{:\implies \red{\boxed{ \blue{ \bf{\mathscr{R}atio = 3 : 7}}}}}$

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Hence, the ratio of height to its diameter is 3:7.