The surface areas of two spheres are in the ratio 16:9 the ratio of their volumes is

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The surface areas of two spheres are in the ratio 16:9 the ratio of their volumes is

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The surface areas of two spheres are in the ratio 16:9 the ratio of their volumes is

5.

If each of two opposite sides of a square is increased by 4 cm and each of other two sides is decreased by 4 cm, we obtain a rectangle of area 84 cm2. What is the perimeter (in cm) of the original square?

A.

40

Let the side of the original square be x cm.According to the question,(x + 4) (x - 4) = 84

The surface areas of two spheres are in the ratio 16:9 the ratio of their volumes is

∴  Perimeter of the original square  = 4a = 4 x 10 = 40 cm

Let  the radius of the two spheres be r and R.

As,

`"Surface area of the first sphere"/"surface area of the second sphere" = 16/9`

`=> (4pi"R"^2)/(4pi"r"^2) = 16/9`

`=> (("R")/"r")^2 = 16/9`

`=> "R"/"r" = sqrt(16/9)`

`=> "R"/"r" = 4/3`        .........(i)

Now,

The ratio of their volumes`= "Volumes of the first sphere"/"Volume of the second sphere"`

`=((4/3pi"R"^3))/((4/3pi"r"^3))`

`=> ("R"/"r")^3`

`=> (4/3)^3`

`=>"R"/"r" = 4/3`            [Using (i)]

`= 64/27`

= 64 : 27

Hence, the correct answer is option (a).