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Related rates for a growing or melting sphere

This type of question, asked 2 times: 14 Jun 2022, 23 Jan 2025. All 2 questions below, oldest first.

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  1. Question 1

    14 Jun 2022

    63
    The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is:

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  2. Question 2

    23 Jan 2025

    134
    A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm , the ice-cream melts at the rate of 81 cm3/min81{\text{ }cm}^{3}/min and the thickness of the ice-cream layer decreases at the rate of 14π cm/min\frac{1}{4\pi}\text{ }cm/min. The surface area (in cm2cm^{2} ) of the chocolate ball (without the ice-cream layer) is :

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