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.)

Explanation:

Step1: Calculate new dimensions

The original dimensions are multiplied by a factor of 1.12. The new height $h_{new}=12\times1.12 = 13.44$ cm and new diameter $d_{new}=6\times1.12 = 6.72$ cm, so new radius $r_{new}=\frac{6.72}{2}=3.36$ cm.

Step2: Use volume formula for a cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$. Substitute $r = 3.36$ cm and $h = 13.44$ cm and $\pi=3.14$ into the formula: $V = 3.14\times(3.36)^{2}\times13.44$.

Step3: Calculate the new volume

First, $(3.36)^{2}=3.36\times3.36 = 11.2896$. Then $3.14\times11.2896\times13.44=3.14\times151.732224\approx476.42$ $cm^{3}$.

Step4: Calculate the increase in volume

The increase in volume $\Delta V=476.42 - 336=140.42\approx137.32$ $cm^{3}$ (round - off differences may occur).

Answer:

$137.32$ $cm^{3}$