a tuna can has a volume..

[breakitdown.]

A tuna can has a volume of 210cm cubed and a base radius of 4.2cm. The company plans to redesign the can with a smaller base. The new can will have the same volume as the original can.

a) Suppose you know the decrease in the base radius. Determine a formula to calculate the increase in height.

b) What is the increase in height for each decrease in the base radius?

i) 0.5 cm ii) 1.0cm


i got;;

a)V=pi r squared * h

210 = pi (4.2)squared*h
210/pi(4.2)squared = h
3.8 = h

Let x = the decrease in the base radius. the radius of the can is now 4.2-x.

the formula for the new height is

210/pi(4.2-x)squared-3.8


b)i) 210/pi(4.2)squared + 210/pi(4.2-0.5)squared-3.8

210/55.4 + 210/39.2 = 3.79+ 5.36
=9.15cm




The correct answer is 1.1cm for part i) and 2.7cm for part ii)


help?

 

[mammothrob]

\(\displaystyle \begin{array}{l}
{\rm Let x = the decrease in the radius} \\
v = \pi r^2 h \\
\\
210 = \pi r^2 h \\
\\
\frac{{210}}{{\pi r^2 }} = h \\
\\
\frac{{210}}{{\pi (4.2)^2 }} = 3.79 \\
\\
{\rm this is the formula for the increase in height} \\
\frac{{210}}{{\pi (4.2 - x)^2 }} - 3.79 = h_1 \\
\end{array}\)