Sphere or balloon: link the rates of its radius, surface area and volume

1. A.
   $\frac{1}{6}\,\text{cm/sec}$
2. B.
   $\frac{1}{36}\,\text{cm/sec}$
3. C.
   $6\,\text{cm/sec}$
4. D.
   $36\,\text{cm/sec}$

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1. A.
   16
2. B.
   6
3. C.
   12
4. D.
   8

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1. A.
   $\dfrac{27\pi}{4}(2x + 3)^2$
2. B.
   $\dfrac{2\pi}{3}(2x + 3)^2$
3. C.
   $\dfrac{27\pi}{8}(2x + 3)^2$
4. D.
   $\dfrac{27\pi}{2}(2x + 3)^2$

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1. A.
   $0.5$ cm/second
2. B.
   $0.25$ cm/second
3. C.
   $0.125$ cm/second
4. D.
   $1$ cm/second

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1. A.
   The radius is increasing at the rate of $\dfrac{1}{2\pi}$ cm/s
2. B.
   The radius is decreasing at the rate of $\dfrac{1}{2\pi}$ cm/s
3. C.
   The radius is increasing at the rate of $\dfrac{1}{\pi}$ cm/s
4. D.
   The radius is decreasing at the rate of $\dfrac{1}{\pi}$ cm/s

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1. A.
   $3$ cm
2. B.
   $5$ cm
3. C.
   $6$ cm
4. D.
   $4$ cm

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1. A.
   $25\pi\ \mathrm{cm^3/sec}$
2. B.
   $50\pi\ \mathrm{cm^3/sec}$
3. C.
   $100\pi\ \mathrm{cm^3/sec}$
4. D.
   $10\pi\ \mathrm{cm^3/sec}$

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1. A.
   $160\pi\ \mathrm{cm^2/sec}$
2. B.
   $1600\pi\ \mathrm{cm^2/sec}$
3. C.
   $16000\pi\ \mathrm{cm^2/sec}$
4. D.
   $16000\ \mathrm{cm^2/sec}$

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