10. [0/1 Points] DETAILS PREVIOUS ANSWERS OSCOLALG1 5.4.295. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the given volume and radius of a cylinder to express the height of the cylinder algebraically. (Simplify your answer completely.) Volume is ?(25x³ - 165x² - 69x - 7), radius is 5x + 1 Recall the formula for the volume V of a cylinder with radius r and height h, V = ?r²h. Note that when ? and the radius are known, the height is the missing factor of the volume. If using synthetic division, what is the binomial divisor and the corresponding value for k? How are multiplication and addition used to complete the process of synthetic division?
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Step 1: The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Show more…
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The height of the cylinder is 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 is A = 2πr h (it's two circles for the top and bottom plus a rolled-up rectangle for the side). Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r, so we can write that as A(r) = 2πr(r + 6). What is the domain of A(r)? In other words, for which values of r is A defined? Part b: Find the inverse function A(r). Your answer should look like some expression involving A.
Supreeta N.
The volume and area of a cylinder are calculated as: Volume = πr2h Area = 2πrh + 2πr2 Given the radius and height of a cylinder as floating-point numbers, output the volume and area of the cylinder. Hint: Use the built-in pow() function and the constant pi from the math module in your calculations. Output each floating-point value with one digit after the decimal point, which can be achieved as follows:print('Volume: {:.1f} cubic inches'.format(yourValue)). Ex: If the input is: 5.2 8.1 where 5.2 is the radius of the cylinder and 8.1 is the height of the cylinder, then the output is: Volume: 688.1 cubic inches Surface area: 434.5 square inches
Shelayah R.
The formula from Exercise 54 has an interesting derivation. The volume of a cylinder is $V=\pi r^{2} h$ while the surface area is given by $S=2 \pi r^{2}+2 \pi r h$ (the circular top and bottom $+$ the area of the side). a. Solve the volume formula for the variable $h$ b. Substitute the resulting expression for $h$ into the surface area formula and simplify. c. Combine the resulting two terms using the least common denominator, and the result is the formula from Exercise 54 d. Assume the volume of a can must be $1200 \mathrm{cm}^{3}$ Use a calculator to graph the function S using an appropriate window, then use it to find the radius $r$ and height $h$ that will result in a cylinder with the smallest possible area, while still holding a volume of $1200 \mathrm{cm}^{3} .$ Also see Exercise 62
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