Question

17. A cylinder has the volume of 400 cm3 and adiameter of 20 cm. Which of the following is closestto the height of the cylinder?A. 1 cmB. 4 cmC. 20 cmD. 40cm

Answer 1

We can relate height and volume using the expression for the volume:

The volume of the cylinder is the product of the base area, a circumference of diameter 20 cm, and the height:

`\begin{gathered} V=((\pi D^2)/(4))\cdot h \\ V=400 \\ D=20 \end{gathered}`
`\begin{gathered} 400=((\pi\cdot20^2)/(4))\cdot h \\ 400=((\pi\cdot400)/(4))\cdot h \\ 400=100\pi\cdot h \\ h=(400)/(100\pi) \\ h=(4)/(\pi) \\ h\approx(4)/(3.14)=1.27\text{ cm} \end{gathered}`

The height for this cyinder is approximately 1.27 cm, so the closest value is 1 cm.

Answer: Option A (1 cm)