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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 = 2rr2 + 27rh (it's two circles for the top and bottom plus a rolled up rectangle for the side). r = radius Areas = n r² h = height Area = h(2rtr) Circumference 2ar

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 = 2rr2 + 27rh (it's two circles for the top and bottom plus a rolled up rectangle for the side). r = radius Areas = n r² h = height Area = h(2rtr) Circumference 2ar

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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 2rr + 2rrh (it's two circles for the top and bottom plus a rolled up rectangle for the side). r = radius Areas = t r? h = height Area = h(2rtr) Circumference 2ar 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 Tr2 + 16 Tr. What is the domain of A (r)? In other words, for which values of r is A (r) defined?
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 2rr + 2rrh (it's two circles for the top and bottom plus a rolled up rectangle for the side). r = radius Areas = t r? h = height Area = h(2rtr) Circumference 2ar 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 Tr2 + 16 Tr. What is the domain of A (r)? In other words, for which values of r is A (r) defined?
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. r(A) = Hints: • To calculate an inverse function, you need to solve for r. Here you would start with A = 2 Tr + 16 tr. This equation is the same as 2 Tr2 + 16 Tr – A = 0 which is a quadratic - equation in the variable r, and you can solve that using the quadratic formula. 3 T+1 x+1 more information in the Introduction to Mobius unit. • If you want to type in in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is Part c: If the surface area is 175 square inches, then what is the rardius r? In other words, evaluate r (175). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as v17.3, 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 The radius is Number inches if the surface area is 175 square inches.
Transcribed Image Text: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. r(A) = Hints: • To calculate an inverse function, you need to solve for r. Here you would start with A = 2 Tr + 16 tr. This equation is the same as 2 Tr2 + 16 Tr – A = 0 which is a quadratic - equation in the variable r, and you can solve that using the quadratic formula. 3 T+1 x+1 more information in the Introduction to Mobius unit. • If you want to type in in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is Part c: If the surface area is 175 square inches, then what is the rardius r? In other words, evaluate r (175). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as v17.3, 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 The radius is Number inches if the surface area is 175 square inches.
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