Question

The diameThe diameter of two silver discs are in the ratio 2:3 . what will be the ratio of their areas?ter of two silver discs are in the ratio 2:3 . what will be the ratio of their areas?

Answer 1

Appropriate Question :

The diameter of two silver discs are in the ratio 2 : 3. what will be the ratio of their areas?

Given :

• Ratio of the diameter of two silver discs = 2 : 3

To find :

• Ratio of their areas

Knowledge required :-

→ Formula to calculate radius :-

• Radius = Diameter/2

→ Formula to calculate area of circle :-

• Area of circle = πr²

where,

• Take π = 22/7
• r = radius of the circle

Solution :

Let the diameter of the two silver discs be 2x and 3x.

Radius (r) = 2x/2 = x

Radius (R) = 3x/2

Area of first silver disc :-

⠀⠀⠀⇒ Area = πr²

⠀⠀⠀⇒ Area = π(x)²

⠀⠀⠀⇒ Area = πx²

Area of the first silver disc = πx²

Area of second disc :-

⠀⠀⠀⇒ Area = π(3x/2)²

⠀⠀⠀⇒ Area = π(9x²/4)

Area of the second disc = π(9x²/4)

Ratio of the areas = Area of the first silver disc/Area of the second disc

⠀⠀

$\longrightarrow \quad \sf{ \dfrac{\pi {x}^{2} }{\pi \frac{9 {x}^{2} }{4} } }$

$\longrightarrow \quad \sf{ \dfrac{ \not\pi {x}^{2} }{ \not\pi \frac{9 {x}^{2} }{4} } }$

$\longrightarrow \quad \sf{ \dfrac{{x}^{2} }{ \frac{9 {x}^{2} }{4} } }$

$\longrightarrow \quad \sf{ \dfrac{{x}^{2} \times 4 }{ {9 {x}^{2} } } }$

$\longrightarrow \quad \sf{ \dfrac{ \not{x}^{2} \times 4 }{ {9 \not{x}^{2} } } }$

$\longrightarrow \quad \sf{ \dfrac{ 4 }{ {9 } } }$

$\red\bigstar \: \underline{ \pmb{ratio \: of \: the \: areas \: of \: the \: \: two \: siver \: discs = 4 :9}}$