Question

17) A brand of coconut oil is updating its packaging. The old rectangular container was 1 foottall, 4 inches long and 2.5 inches wide, their new cylindrical container has a 4.5 centimeterradius and is 30 centimeters tall.a) Determine the volume of the rectangular container, 3 points(if needed round the final answer to the nearest hundredth.)b) Determine the volume of the cylindrical container. 3 points(if needed round the final answer to the nearest hundredth.)c) The company charges the same amount for each container. Is one of the containers abetter buy? Explain and show work that justifies your answer. 3 points

Answer 1

a) Volume of rectangular container:

1 foot = 12 inches

$\begin{gathered} V=\text{tall}\times long\times wide \\ V=12\times4\times2.5 \\ V=120inches^3 \end{gathered}$

b) Volume of the cylindrical container:

$\begin{gathered} V=\pi\times r^2\times h \\ V=\pi\times(4.5)^2\times30 \\ V=\pi\times20.25\times30 \\ V=607.5\pi \\ V=607.5(3.14) \\ V=1907.55\operatorname{cm}^3 \end{gathered}$

c) First, we convert the volumes of the containers into the same units.

For volume of the rectangular container in centimeters:

1 inch3 = 16.3871 cm3

$V=120\times16.3871=1966.45\operatorname{cm}^3$

With this, we can say that the rectangular container has a larger volume than the cylindrical container. Therefore, the cylindrical container is a better buy.

Answer:

a) V = 120 in^3

b) V = 1907.55 cm^3

c) Cylindrical container is a better buy