Respuesta :

Answer:

surface area of a sphere= 4pi*r^2

S.A when radius is 7 is:

=4pi*(7)^2

=196pi cm^2

if you multiply radius by 4, the equation becomes:

4pi*(4r)^2

=4pi*16r^2

=64pi*r^2

substitute 7 into equation:

=64pi*(7)^2

=64pi*49

=3136pi cm^2

Divide new S.A. by old S.A. to show effect:

=3136pi/196pi

=16

If the radius is multiplied by 4, the effect on the surface area is that it is 16 times the surface area of the sphere where the radius is not multiplied.

If the radius of a sphere of radius 7 cm is multiplied by 4, then its surface area is increased 16 times than the initial surface area.

How to find the surface area of a sphere?

Suppose that radius of the considered sphere is of 'r' units.

Then, its surface area S would be:

[tex]S = 4\pi r^2 \: \rm unit^2[/tex]

For this case, we're specified that:

  • Initial radius of sphere = 7 cm
  • Final radius of sphere = 4 × 7 =  28 cm.

We've to find the effect on the surface area of the sphere.

Initial surface area:

[tex]S_i = 4\pi r^2 = 4 \pi (7)^2 \: \rm unit^2[/tex]
Final surface area:

[tex]S_f = 4\pi r^2 = 4 \pi (4 \times 7)^2 = 4^2 \times [4 \pi (7)^2] \: \rm unit^2\\\\S_f =16 \times S_i[/tex]

Thus, if the radius of a sphere of radius 7 cm is multiplied by 4, then its surface area is increased 16 times than the initial surface area.

Learn more about surface area of sphere here:

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