Question

question 6 (multiple choice worth 1 points) (06.02 mc) 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. o 476.44 cm³ o 137.32 cm³ o 815.56 cm³ o 379.81 cm³

Explanation:

Step1: Recall the volume - scaling formula

If the linear dimensions of a three - dimensional object are scaled by a factor \(k\), the volume of the object is scaled by a factor \(k^{3}\). Here, \(k = 1.12\).

Step2: Calculate the new volume

The current volume \(V_1=339.12\ cm^{3}\). The new volume \(V_2\) is given by \(V_2=V_1\times k^{3}\). Substitute \(V_1 = 339.12\) and \(k = 1.12\) into the formula: \(V_2=339.12\times(1.12)^{3}\). First, calculate \((1.12)^{3}=1.12\times1.12\times1.12 = 1.404928\). Then, \(V_2=339.12\times1.404928\approx476.44\ cm^{3}\).

Answer:

D. \(476.44\ cm^{3}\)