Question

if the radii of the sphere is increase by 100%, the volume of corresponding sphere is increase by​

Answer 1

Answer:

300%

Step-by-step explanation:

Given---> The radius of the sphere is increase by 100% .

To find---> Increase in volume of sphere.

Solution---> We know that,

Surface area of sphere = 4 π ( radius )²

Let initial radius of sphere be r.

Initial surface area ( S₁ ) = 4 π r²

ATQ, % increase in radius of sphere = 100%

Increase in radius = r × 100 / 100

= r

New radius of sphere = old radius + increase in radius

= r + r

= 2r

New surface area ( S₂ ) = 4 π ( radius )²

S₂ = 4 π ( 2r )²

= 4 π ( 4r² )

S₂ = 16 π r²

Increase in surface area = S₂ - S₁

= 16 π r² - 4 π r²

= 12 π r²

% increase in surface area

=( Increase in surface area/old surface area )× 100

% increase in surface area = ( 12 π r² / 4π r² )× 100

= 3 × 100

= 300 %

Answer 2

Answer:

700%

Step-by-step explanation:

Let V1 and R1 be the volume and radius of the initial sphere respectively.

→ V1 = 4/3 $\pi R1^{3}$

Let R2 be the increased radius and V2 be the volume of the new sphere.

R2 = R1+(100% of R1)

     = 2R1

V2 = 4/3 $\pi R2^{3}$

     =4/3 $\pi (2R1)^{3}$

     =4/3$\pi *8*(R1)^{3}$

     =8*V1

V2 - V1 = 8 V1 - V1

            =7 V1

percentage of increase in the volume of the new sphere = [(V2-V1)/V1] *100

                          = [(7V1)/V1]*100

                          =700%

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