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. 476.44 cm3 137.32 cm3 815.56 cm3 379.81 cm3

Answer 1

To find out how much more the new cans will hold, we need to calculate the volume of the new cans and then subtract the volume of the current cans from it. The new cans will hold 233.78 cm³ more than the current cans.

Step-by-step explanation:

To find out how much more the new cans will hold, we need to calculate the volume of the new cans and then subtract the volume of the current cans from it. The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height. Since the diameter of the current cans is 6 cm, the radius is half of that, which is 3 cm. The height is 12 cm. So, the volume of the current cans is V = 3.14 × (3 cm)² × 12 cm = 339.12 cm³. Now, let's calculate the volume of the new cans. Since the dimensions of the new cans are increased by a multiple of 1.12, the new height will be 12 cm * 1.12 = 13.44 cm. The new diameter will be 6 cm * 1.12 = 6.72 cm, and the new radius will be 3.36 cm. Substituting these values into the volume formula, we get V = 3.14 × (3.36 cm)² × 13.44 cm = 572.90 cm³. Finally, to find out how much more the new cans will hold, we subtract the volume of the current cans from the volume of the new cans: 572.90 cm³ - 339.12 cm³ = 233.78 cm³.

Therefore, the new cans will hold 233.78 cm³ more than the current cans.