Question

the sum of the height and diameter of a cylinder is 24 cm. what is the maximal volume of the cylinder?

Answer 1

\[22/7\times23\times1\]

Answer 2

how did u get the answer please ?

Answer 3

You can find the maximum volume by differentiation.
Find the critical point, V'(r)=0

well, \[2\pi r+h=24cm\]
therefore, \[h=24-2 \pi r\]

and the volume of the cylinder is\[v(r)=\pi r^2h=\pi r^2(24-2 \pi r)\]
you differentiate this, \[v'(r)=48 \pi r-6 \pi^2 r^2=0\]
Therefore, \[\pi r=8\](or 0 but it is unreasonable cause neither r and pi is not 0)

So,\[2 \pi r=16cm, h=8cm, r=2.55cm\]

The answer is v=3.14*(2.55)^2*8=163.34cm^3

But I don't know this is right or wrong. Sorry :)

Answer 4

thank you