Question

The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is
(a)1 : 2
(b)2 : 3
(c)9 : 16
(d)16 : 9

Answer 1

Answer:

The Ratio of their curved surface area is 16 : 9.

Among the given options option (d) 16 : 9 is the correct answer.

Step-by-step explanation:

Given :  

Volumes of two spheres in the ratio = 64 : 27  

V1 : V2 = 64 : 27  

 

Let the radius of first sphere be r1 and radius of second sphere be r2.

 

V1 / V2 = 64 / 27  

64/27 = (4/3 πr₁³) / (4/3 πr₂³)  

64/27 = r₁³/r₂³  

4³/3³ = r₁³/r₂³

(r₁/r₂)³ = (4/3)³

r₁/r₂ = 4/3 …. ……..(1)

 

Ratio of their curved surface area :  

curved surface area first sphere, S1 : curved surface area second sphere ,S2= 4πr1² : 4πr2²

S1/S2 = 4πr1²/4πr2²

S1/S2 = r1²/r2²

S1/S2 = (r1/r2)²

S1/S2 = (4/3)²

[FROM EQ 1]

S1/S2 = 16 / 9

S1: S2 = 16 : 9

Ratio of their curved surface area = 16 : 9

Hence, the Ratio of their curved surface area is 16 : 9.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer :- 16 :9✔️✔️

EXPLANATION : -

Ratio of volumes = (R^3):(r^3)=64:27

=( 4^3) : (3^3)

so, (R) :(r) = 4:3

ratio of surface areas =(R^2) : (r^2)

= (4^2) :(3^2)

=16:9✔️✔️✔️

✌✌✌✌✌✌✌✌

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