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A sphere has a radius of 6 inches and a surface area of 144rt in The radius of the sphere will be doubled
How will this effect the surface area of the sphere?
It will be tripled
It will be doubled.
It will be the same.
It will be quadrupled

Respuesta :

calculista

Answer:

It will be quadrupled

Step-by-step explanation:

we know that

All spheres are similar

so

The ratio of the surface areas of two spheres is equal to the scale factor squared

Let

z ----> the scale factor

x ----> surface area of the sphere with radius doubled

y ----> surface area of the original sphere

so

[tex]z^2=\frac{x}{y}[/tex]

[tex]x=(z^2)y[/tex]

The scale factor is 2 (because the radius of the sphere will be doubled)

[tex]z=2[/tex]

substitute

[tex]x=(2^2)y\\x=4y[/tex]

so

The new surface area is 4 times the original surface area

therefore

The surface area will be quadrupled

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