Question

topic 2 composing and decomposing functions
skills practice continued
problem set 3: exploring cubic functions

complete each table. include an expression for the volume. circle the relative maximum or

minimum if there is one.
1

2

Explanation:

Step1: Calculate height of cylinder

The height of the cylinder is given by the formula \(h = 3r\).
For \(r = 0.5\), \(h=3\times0.5 = 1.5\)
For \(r = 1\), \(h = 3\times1=3\)
For \(r = 2\), \(h=3\times2 = 6\)
For \(r = 3\), \(h=3\times3=9\)
For \(r = 4\), \(h=3\times4 = 12\)

Step2: Calculate base area of cylinder

The base area of the cylinder is given by the formula \(A = 3.14r^{2}\).
For \(r = 0.5\), \(A=3.14\times(0.5)^{2}=3.14\times0.25 = 0.785\)
For \(r = 1\), \(A=3.14\times(1)^{2}=3.14\)
For \(r = 2\), \(A=3.14\times(2)^{2}=3.14\times4 = 12.56\)
For \(r = 3\), \(A=3.14\times(3)^{2}=3.14\times9 = 28.26\)
For \(r = 4\), \(A=3.14\times(4)^{2}=3.14\times16 = 50.24\)

Step3: Calculate volume of cylinder

The volume of the cylinder is given by the formula \(V=A\times h\) (where \(A\) is the base area and \(h\) is the height).
For \(r = 0.5\), \(V=0.785\times1.5=1.1775\)
For \(r = 1\), \(V=3.14\times3 = 9.42\)
For \(r = 2\), \(V=12.56\times6=75.36\)
For \(r = 3\), \(V=28.26\times9 = 254.34\)
For \(r = 4\), \(V=50.24\times12=602.88\)

Answer:

Radius of Cylinder (in.)	Height of Cylinder (in.)	Base Area of Cylinder (in.²)	Volume of Cylinder (in.³)
\(0.5\)	\(1.5\)	\(0.785\)	\(1.1775\)
\(1\)	\(3\)	\(3.14\)	\(9.42\)
\(2\)	\(6\)	\(12.56\)	\(75.36\)
\(3\)	\(9\)	\(28.26\)	\(254.34\)
\(4\)	\(12\)	\(50.24\)	\(602.88\)
\(r\)	\(3r\)	\(3.14r^{2}\)	\(9.42r^{3}\)