Math 205 - Calculus I
Homework due October 21
Question 1. Bob is blowing air into a spherical balloon. Since the balloon is inflating, the
volume V(t), surface area S(t), and the radius r(t) of the balloon are all changing as functions
of time (increasing in all three cases).
(a) When the radius is 10 cm, Bob knows that he is blowing in air at a rate of 5cm3
min .
Use the concept of related rates to find at what rate the radius is changing at the moment
that r= 10 cm. [Hint: Look up the formula for the volume enclosed by a sphere of radius
r.]
(b) When the radius is 15 cm, Bob knows that the radius is increasing at a rate of 2 cm/sec.
Use the concept of related rates to find at what rate the surface area is changing when
r= 15 cm. [Hint: Look up the formula for the surface area of a sphere of radius r.]
Question 2. Bob was cooking pancakes one morning while writing a homework for his calculus
class. As he was pouring the pancake batter onto the skillet, he noticed that the batter would
form into a circular shape and grow concentrically as he poured more batter. He also noticed
that when the radius of the pancake was 3 inches, the area was growing at a rate of 10 square
inches per second. He wondered if he could figure out how fast the radius was growing at that
point, but instead he decided to assign it for homework. So, when the radius is 3 inches, how
fast is the radius of the pancake growing? [Hint: What is the equation for the area of a circle
in terms of the radius?]
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