Question

The Curved Surface Area of a cylinder is 264 m² and its volume is 924 m³. What is the ratio of its diameter to its height ?​

Answer 1

$\Large{\underline{\underline{\textbf{Answer :-}}}}$

The Ratio of its diameter to its Height is 7 : 3.

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$\Large{\underline{\underline{\textbf{Explanation :-}}}}$

Given :

Curved surface area of a cylinder = 264 cm²

Volume of the cylinder = 924 cm³

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C.S.A of a cylinder = 264 cm²

→ 2πrh = 264 cm²

→ rh = $\dfrac{264}{2π}$

→ rh = $\dfrac{264}{2} \times \dfrac{22}{7}$

→ rh = $\dfrac{(264 × 7)}{(44)}$

→ rh = 6 × 7  

→ rh = 42 cm ……..(1)

 

Volume of the cylinder = 924 cm³

→ πr²h = 924 cm³

→ πr(rh) = 924 cm³

→ $\dfrac{22}{7}$ × r × 42 = 924   [From eqⁿ 1]

→ 22r × 6 = 924

→ 132r = 924

→ r = $\dfrac{924}{132}$

→ r = 7 cm

Radius of the cylinder = 7 cm  

[ On putting the value of r = 7 cm in eqⁿ 1 ]

→ rh = 42 cm

→ 7 × h = 42

→ h = $\dfrac{42}{7}$

→ h = 6 cm

Height of a Cylinder =  6 cm  

Diameter of a Cylinder = 2 × Radius  

→ d = 2 × 7  

→ d = 14 cm

Ratio of its diameter to its Height = d : h  

→ d : h = 14 : 6  

→ d : h = 7 : 3  

Hence, the Ratio of its diameter to its Height is 7 : 3.

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