The height of the cylinder is 8 inches. We'll be analyzing the surface area of a round cylinder - in other words the amount of material needed to "make a can". A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A, is A = 2nr2 + 2arh (it's two circles for the top and bottom plus a rolled up rectangle for the side). Areas xr² r = radius Circumference 2xr T (A) = h = height O Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we can write that as A (r) = 2 ² + 16 r. What is the domain of A (r)? In other words, for which values of r is A (r) defined? Area h(2x) Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A. This is the inverse function to A (r), i.e to turn A as a function of r into. r as a function of A. The radius is Number Hints: • To calculate an inverse function, you need to solve for r. Here you would start with A 2 nr2 + 16 r. This equation is the same as 2 r2 + 16 ar-A=0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula. If you want to type in 3+1 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is 2+1 more information in the Introduction to Mobius unit. Part c: If the surface area is 225 square inches, then what is the rardius r? In other words, evaluate r (225). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as √17.3, you could • Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in -sqrt(17.3) . Use a browser to connect to the Internet and type in sqrt(17.3) into a search field . Use a calculator inches if the surface area is 225 square inches.
The height of the cylinder is 8 inches. We'll be analyzing the surface area of a round cylinder - in other words the amount of material needed to "make a can". A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A, is A = 2nr2 + 2arh (it's two circles for the top and bottom plus a rolled up rectangle for the side). Areas xr² r = radius Circumference 2xr T (A) = h = height O Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we can write that as A (r) = 2 ² + 16 r. What is the domain of A (r)? In other words, for which values of r is A (r) defined? Area h(2x) Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A. This is the inverse function to A (r), i.e to turn A as a function of r into. r as a function of A. The radius is Number Hints: • To calculate an inverse function, you need to solve for r. Here you would start with A 2 nr2 + 16 r. This equation is the same as 2 r2 + 16 ar-A=0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula. If you want to type in 3+1 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is 2+1 more information in the Introduction to Mobius unit. Part c: If the surface area is 225 square inches, then what is the rardius r? In other words, evaluate r (225). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as √17.3, you could • Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in -sqrt(17.3) . Use a browser to connect to the Internet and type in sqrt(17.3) into a search field . Use a calculator inches if the surface area is 225 square inches.
Chapter3: Polynomial Functions
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Transcribed Image Text:The height of the cylinder is 8 inches.
We'll be analyzing the surface area of a round cylinder - in other words the amount of material needed to
"make a can".
A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the
radius of the top of the can and let h be the height. The surface area of the cylinder, A, is
A = 2² + 2πrh (it's two circles for the top and bottom plus a rolled up rectangle for the side).
Areas = r²
T(A) =
r-radius
Circumference
2πr
Hints:
h = height
O Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we can
write that as A (r) = 2 r² + 16 r. What is the domain of A (r)? In other words, for which values of
r is A (r) defined?
Area h(2)
Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function
of A. This is the inverse function to A (r), i.e to turn A as a function of r into. r as a function of A.
=
The radius is Number
DO
To calculate an inverse function, you need to solve for r. Here you would start with
A = 2 ² + 16 Tr. This equation is the same as 2 r2 + 16 Tr-A=0 which is a quadratic
equation in the variable r, and you can solve that using the quadratic formula.
. If you want to type in
in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is
x+1
more information in the Introduction to Mobius unit.
Part c: If the surface area is 225 square inches, then what is the rardius r? In other words, evaluate
r (225). Round your answer to 2 decimal places.
Hint: To compute a numeric square root such as ✓17.3, you could
• Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in -sqrt(17.3)
• Use a browser to connect to the Internet and type in sqrt(17.3) into a search field
. Use a calculator
inches if the surface area is 225 square inches.
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