1) A spherical snowball is melting in such a way that its radius is decreasing a

Question

1) A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.2 cm/min. At what rate is the volume of the snowball decreasing when the radius is 8 cm. (Note the answer is a positive number).

answer:____________cm^3/min

answer:________cm/min

3)At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 21 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 3 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

answer:_____knots

*please show steps! Thank you!

Explanation / Answer

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

dV/dt= 4pi*r^2*dr/dt

putting values dr/dt = 160.8495 cm^3/min.

2)A=1/2 * b * h

dA/dt = 1/2 *(b*dh/dt + h*db/dt)

also, Area=94cm^2 and h=8.5 cm

So, b=2A/h = 22.1176 cm.

putting values and solving

db/dt=-2.131 m/min.

3)distance(S)=(40+21t)i + 24t j

So, dS/dt=21 i + 24 j

So, magnitude = sqrt(21^2 + 24^2)

=31.89 knots.

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