/ The radius of a semicircle is increasing at the rate of 0.8 cm/s. Calculate the rate of change in the area and the perimeter of the semicircle when the radius is 5 cm
/ The radius of a semicircle is increasing at the rate of 0.8 cm/s. Calculate the rate of change in the area and the perimeter of the semicircle when the radius is 5 cm
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 45SE: A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the...
Related questions
Question
30..answer no 1 do like example 6 solution
Transcribed Image Text:TUTORIAL 30
The radius of a semicircle is increasing at the rate of 0.8 cm/s. Calculate the rate of
change in the area and the perimeter of the semicircle when the radius is 5 cm
2 A stone dropped into a still pond sends out a circular ripple whose area increases at a
rate of 5 cm'/s. How fast is the radius of the ripple changing when the radius is 2 cm ?
3 Oil from a leaking oil tanker radiates outward in the form of a circular film on the surface
of the water. If the area of the circle increases at the rate of 400 m'/min, how fast is the
radius of the circle increasing when the area is 1225n m.
4. The radius, rcm of a circle at time t is given by r = 21 + 3. Determine the rate of
change in the area when t = 1. (Give your answer in terms of n).
5. The area of a semicircle is increasing at the rate of 4n cm s'.
Calculate the rate of change in the radius of the semicircle when the radius is 5 cm.
6. Oil spilled from a ruptured tanker spreads in a circle whose radius inreases at a
constant rate of 2 cm/s. How fast is the area of the spill increasing after 5 minutes ?
1. A closed cuboid has a square base and its height is twice its base. If x is the length of
the base and x increases at a rate of 3 cm s, find the rate of change of the
surface area when x is 4 cm.
8. At what rate is the volume and surface area of a cube is changing when the side is 15
cm and each side is increasing at the rate of 0.6 cm/sec.
9. The radius of a spherical balloon increases at a rate of 0.2 cms.
How fast is the volume changing at a certain instant when its volume is 288t cm.
10. A spherical balloon is to be deflated at a rate of p cm's'. The radius of the balloon
decreases ata rate of 0.5 cms when its volume is 288t cm.
Find the value of p.
11. A boy is blowing a spherical balloon at a rate of 50 cm/s. At what rate is the radius of
the balloon changing when the radius is 10 cm.
12. The surface area of a sphere decreases at a rate of 5 m's. How fast is the radius
changing when the radius is 3 m.
13. If the radius of a sphere is increasing at the constant rate of 2 mm per sec, how fast is
the volume changing when the surface area is 8 mm ?
4.
(Hint: Vaphiere = r: Agphere = 4nr")
Answers:
dA
4( 2)
de
40
Transcribed Image Text:Example 6:
A cuboid metal slab has a width of x m, length 2x m and height 2 m.
2 m
2x m
When heated, the widih expanded at the rate of 0.01 mh.
Find the rate of change of the surface area when the volume is 36 m,
Solution:
dA
dx
= 0.01.
dt
= ?, V = 36
dt
V =
4x
4x =
36
x =
2 ( 2x + 4x + 2x)
4x + 12x
A
%3D
dA
dx
dA
%3D
dt
dt
dx
0.01 x (8x + 12)
%3!
0.01 x (8(3) + 12)
0.36 m2 h
%3D
Alternative Solution:
A =
4x + 12x
dA
dt
dx
dx
+ 12
dt
8x
%3D
dt
8(3)(0.01) + 12 (0.01)
0.36 m h
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