A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 7 cm/s. Express the surface area of the balloon as a function of time t (in seconds). (Let S (0) = 0.). S (t) = cm^2?

Question

Mathematics

Claire Roberts

19 February, 13:54

A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 7 cm/s. Express the surface area of the balloon as a function of time t (in seconds). (Let S (0) = 0.). S (t) = cm^2?

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Answers (1)

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Raiden Stanton · Answer 1

R (t) = 6t

putting into the formula

V = (4/3) pi * r^3

V (t) = (4/3) pi * (6t) ^3

V (t) = (4/3) pi * 216 t^3

Multiply the 4/3 by the 216 and

V (t) = 288 * pi * t^3