Question

as part of a new advertising campaign, a beverage company wants to increase the dimensions of their cans by a multiple of 1.12. if the cans are currently 12 cm tall, 6 cm in diameter, and have a volume of 339.12 cm³, how much more will the new cans hold? use 3.14 for π and round your answer to the nearest hundredth. 379.81 cm³ 815.56 cm³ 137.32 cm³ 476.44 cm³

Explanation:

Step1: Find the original volume formula for a cylinder

The volume formula for a cylinder is $V = \pi r^{2}h$, where $r$ is the radius and $h$ is the height. Given the original diameter $d = 6$ cm, the original radius $r=\frac{d}{2}=3$ cm and height $h = 12$ cm. The original - volume $V_1=\pi r^{2}h=3.14\times3^{2}\times12=3.14\times9\times12 = 339.12$ $cm^{3}$.

Step2: Calculate the new dimensions

The dimensions are increased by a multiple of 1.12. The new radius $r_2=3\times1.12 = 3.36$ cm and the new height $h_2=12\times1.12 = 13.44$ cm.

Step3: Calculate the new volume

Using the volume formula $V=\pi r^{2}h$, the new volume $V_2 = 3.14\times(3.36)^{2}\times13.44$. First, $(3.36)^{2}=3.36\times3.36 = 11.2896$. Then $V_2=3.14\times11.2896\times13.44=3.14\times151.732224\approx476.44$ $cm^{3}$.

Step4: Find the difference in volume

The difference in volume $\Delta V=V_2 - V_1$. Substituting the values, $\Delta V=476.44 - 339.12=137.32$ $cm^{3}$.

Answer:

$137.32$ $cm^{3}$