For the following exercises, determine the function described and then use it to answer the question. 64. The volume of a right circular cone, V , in terms of its radius, r , and its height, h , is given by V = 1 3 π r 2 h . Express r in terms of h if the height of the cone is12 feet and find the radius of a cone with volume of50 cubic inches.
For the following exercises, determine the function described and then use it to answer the question. 64. The volume of a right circular cone, V , in terms of its radius, r , and its height, h , is given by V = 1 3 π r 2 h . Express r in terms of h if the height of the cone is12 feet and find the radius of a cone with volume of50 cubic inches.
For the following exercises, determine the function described and then use it to answer the question.
64. The volume of a right circular cone, V, in terms of its radius, r, and its height, h, is given by
V
=
1
3
π
r
2
h
.
Express r in terms of h if the height of the cone is12 feet and find the radius of a cone with volume of50 cubic inches.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
Let V represent the volume of a cone with radius r cm and height h cm. Write an equation for V (in cm) in terms of r and h.
V=
cm3
Find the radius of a cone (in cm) when its diameter is 4 m.
cm
Find the value of h (in cm) if the height is known to be 2 m.
cm
Water is leaking out of an inverted conical tank at a rate of 10,500 cm/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is
4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate (in cm/min) at which water is being pumped into the tank. (Round your answer to the nearest integer.)
cm³/min
1/3
The radius r of a sphere is given by the equation r =
where Vis the volume of the sphere. Find the radius of the
sphere when
V = 367 cubic feet.
Water is flowing into a conical cistern at the rate if 8 cubic m/min. If
the height of the inverted cone is 12 m, and the radius of its circular
opening is 6 m.
6 m
12 m
48. Which of the following functions is the
correct representation of the Volume of the conical cistern when
the water is 4 meters deep?
A. V = πh³
C. V = Th³
B. V = Th³
D. V = 1/2 Th³
49. How fast is the water level rising when the
water is 4m deep?
A. 0.637 m/min
C. 2.637 m/min
B.1.637 m/min
D. 3.637 m/min
50. What is the rate of the increase in radius
over time when the water is 4m deep?
A. 0.319 m/min
C. 2.319 m/min
B. 1.319 m/min
D. 3.319 m/min
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
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