A circular cylinder, open at one end, has radius r cm and external surface area 27\pi cm^{3}. (i) Show that the volume of the cylinder, V cm^{3}, is given by V=\frac{\pi}{2}(27r-r^{3}).
(ii) Given that r can vary, find the stationary value of V and determine whether this value is a maximum or a minimum.

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answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

nlgqer

step-by-step

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb