vanneSmarifalcep vanneSmarifalcep

20-09-2016
Mathematics

contestada

Given a sphere of diameter, d. What is the percentage increase in its volume when surface area increases by 21%?

Respuesta :

Hussain514 Hussain514

24-09-2016

S1 = Pi * D1^2
solve for D1
D1 = sqrt( S1 / pi ) S2 = Pi * D2^2
S2 = 1.21*S1
S2= 1.21 * Pi * D1^2
1.21 * Pi * D1^2=
Pi * D2^2
D2 D2 = sqrt( 1.21 * D1^2)
Now V2 = pi/6 * D2^3. V2
= pi/6 ( sqrt(1.21*D1^2))^3 V2
= pi/6 * (1.21 * D1^2)^(3/2) V2
= pi/6 * 1.21^(3/2) * D1 ^3 = (pi/6 * D1^3) * 1.21^3/2 = V1 * 1.21 ^(3/2)
=43% approximately

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