Question

The radii of two spheres are in ratio 1:2. The ratio of their surface area will be?​

Answer 1

$\huge \mathfrak \red{answer}$

$\bf{ \huge{ \boxed{ \underline{ \green{ \tt{ \frac{1}{4} \: }}}}}}$

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$\huge \mathfrak{question}$

⟹The radii of two spheres are in ratio 1:2. The ratio of their surface area will be?

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Step by step explanation:

Given:

$⟹ \sf{the \: ratio \: of \: radius \: is1:2}$

$\sf{⟹surface \: area \: of \: sphere = 4\pi {r}^{2}}$

then

Given:

$\sf{⟹ \frac{r1}{r2} = \frac{1}{2}}$

$\rm{surface \: area \: of \: sphere = }$

$\rm{ = \frac{4\pi {r1}^{2} }{4\pi {r2}^{2} }}$

$\rm{⟹ \frac{ {1}^{2} }{ {2}^{2} }}$

$\rm{⟹ \frac{1}{4}}$

The ratio of surface area will be =

$\sf{ \frac{1}{4}}$

Answer 2

Given

Radius of two spheres = 1 : 2

To find

Ratio of their surface area.

Solution

Here, ratio of radius of two spheres are 1 : 2

⟼ r₁ : r₂ = 1 : 2

⟼ r₁ = 1 & r₂ = 2

We know that,

➥ Surface area of sphere = 4πr²

Therefore,

➙ Ratio of the surface areas of two spheres :

⇰ 4πr₁² : 4πr₂²

Putting values :

➻ Ratio = 4π(1)² : 4π(2)²

➻ Ratio = 4π(1)²/4π(2)²

• Cancelling out 4π from both :

➻ Ratio = 1/2²

➻ Ratio = 1/4

➻ Ratio = 1 : 4

Therefore,

Ratio of surface areas of two spheres = 1 : 4 .