Question

5. Volumes of two spheres are in the ratio 64:27. What is the ratio of their
surface area.
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Answer 1

Step-by-step explanation:

let V and V' be the volume of sphere A and sphere B

given V / V' = 64 / 27 ---------------- (@)

let A and A' be the areas of sphere A and sphere B and

let R and R' be the radius of sphere A and sphere B

Now volume of sphere A is given by

V = 4/3πR^3 --------------------------------- (1)

volume of sphere B is given by

V' = 4/3πR'^3 u R'^3 ( using equation @)

R / R' = (64/27)^1/3

R / R' = 4/3 ---------------------------------- (2)

which is radius ratio is 4:3.

now

let A and A' be the surface areas of sphere A and sphere B

we have to find the ratio of surface area.

A / A' = 4πR^2 / 4πR'^2

= R^2 / R'^2

= (R / R') ^2

A / A' = (4 / 3) ^2 ( putting value of R/R' equation (2) )

= 16 / 9

so surface area ratios is 16:9.

Answer 2

Answer:

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