A stack of one dozen cookies of diameter 2.5 in. exactly fits in a cylindrical container of volume 29.452 in3. Which is the thickness of each cooke?

Respuesta :

The volume of a cylinder is given by:

[tex]\begin{gathered} V=\pi\cdot r^2\cdot h \\ V=29.452in^3_{} \\ r=\frac{d}{2}=\frac{2.5}{2}=1.25 \end{gathered}[/tex]

solve for h:

[tex]\begin{gathered} 29.452=\pi\cdot(1.25)^2\cdot h \\ h=\frac{29.452}{\pi(1.25)^2} \\ h=5.999912171 \end{gathered}[/tex]

divide the height by 12:

[tex]\frac{h}{12}=0.499992681in[/tex]

The thickness of each cookie is 0.499992681in or approximately 0.5in