3 авг. 2017 г. · It makes sense that 4πr2 is the surface area since the then 4πr2dr is the volume of a spherical shell, which represents the added volume.

26 сент. 2015 г. · Recall that the volume, surface area and diagonals are given by V=abc,S=2ab+2bc+2ca,D=√a2+b2+c2. I'll do the volume, and then it should be clear ...

29 нояб. 2015 г. · Rectangular box without a top has a volume of 216 in 3. Find dimensions of the box with the smallest surface area. Use second derivative test.

17 окт. 2014 г. · a) Show that the surface area in cm2 is given by A=x2+432/x. b) Use calculus to find the minimum surface area of the box, justifying your answer ...

30 апр. 2014 г. · The area of a square depends on the length of its side. The derivative measures the rate at which the area changes when the side changes, ...

30 апр. 2017 г. · I have recently realized that the first derivative of the area of a circle A=πr2 is the circumference (perimeter) C=2πr and the first derivative ...

24 окт. 2019 г. · The derivative is what it is for the circle (sphere) because you can compute the area (volume) as a sum of thin annuli (spherical shells).

2 апр. 2012 г. · " The variable l is length, the variable w is width, and the variable h is height. Using these, the total area is actually. 2(l×h)+2(w×h)+w ...

20 окт. 2022 г. · Two of these rectangles are rising above the w dimension of the base. Thus, area of one such rectangle is wh. Area of both these rectangles is ...

30 дек. 2018 г. · We have. P=2(l+w)⟹100=2(l+w)⟺50=l+w. A=lw. Rewriting (1) in terms of w (you could do so in terms of l), you'd get. w=50−l.