
Finding rate of change
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Finding rate of change
Last updated at April 19, 2021 by Teachoo
Ex 6.1, 13 A balloon, which always remains spherical, has a variable diameter 3/2 (2π₯ +1). Find the rate of change of its volume with respect to π₯.Let d be the diameter of the balloon Given that Diameter = d = 3/2 (2x + 1) Let r be the radius of the balloon r = π/2 = π/π (2x + 1) The balloon is a spherical Volume of the balloon = 4/3 ππ^3 We need to find rate of change of volume with respect to x i.e. ππ/ππ₯ Now, ππ/ππ₯ = π/ππ₯ (4/3 ππ^3 ) = 4π/3 Γ (ππ^3)/ππ₯ = 4π/3 Γ π/ππ₯ (27/64 (2π₯+1)^3 ) = 9π/16 Γ (π(2π₯ + 1)^3)/ππ₯ = 9π/16 Γ 3(2x + 1)2 Γ 2 = πππ /π (ππ+π)^π