Question

Q4) If the radius of a sphere is
doubled, then what is the ratio of
their surface area?
O 12
O 2:1
O 14
O
4:1​

Answer 1

Let :

• Original radius of sphere = x
• New radius of sphere = y

Given :

• Radius of sphere is double, this means new Radius is twice of original radius

To find :

Ratio of surface area of original sphere to new sphere

Formula used :

Surface area of sphere = 4π r²

Solution :

(1) Original sphere

• Radius = x

• Surface area of original sphere = S (let)
• S = 4π(x)²

(2) New sphere

• Radius = y

• Surface area of new sphere = S' (let)
• S' = 4π (y)²

Also , we are given that new radius = 2× original radius

➝ y = 2x

this gives,

➝ S' = 4π (2x)²

➝ S' = 4π (4x²)

Now , we need to find ratio of surface area of Original sphere to surface area of new sphere

$\sf \implies \: S : S' \: = \: 4\pi( {x}^{2} ) \: : \: 4\pi \: ( 4{x}^{2} ) \\ \\ \sf \implies \: S : S' \: = \: 1 \: : 4$

ANSWER :

Option (3) 1 : 4

Answer 2

$\huge\bf\underline\mathfrak\green{ ‡Required\: Answer}$

(iii) 1 : 4

________________________________

$\bf\underline\green{Step\: by\: step\: explanation :}$

• Let Original radius of sphere is x and New radius of sphere be y.

$\bf\underline\green{Given :}$

• Radius of sphere is doubled, which means new radius is two times more than original radius.

$\bf\underline\green{☆ Lets\: start :}$

$\bf\underline{We\: know\: that:}$

Surface area of sphere = 4π r²

$\bf\underline\green{(i) Original\: sphere :}$

• Radius = x
• Surface area of Original sphere = S
• S = 4π(x) ²

$\bf\underline\green{(ii) New sphere :}$

• Radius = y
• Surface area of New\: sphere = S'
• S' = 4π (y)²

________________________________

It is given that new radius = 2 × original radius.

→ y = 2x

this shows that,

• S' = 4π (2x)²

• S' = 4π (4x²)

________________________________

Come on, Lets find the ratio of surface area of the Original sphere to Surface area of New sphere.

↝ S : S = 4π(x²) : 4π(4x²)

↝ S : S' = 1 : 4

________________________________

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