Question

A food company distributes its tomato soup in two cans of different sizes. For the larger can, both the diameter and the height have been increased by 15%.By what percentage does the volume increase from the smaller can to the larger can? Round your answer to the nearest percent.

Answer 1

Problem

A food company distributes its tomato soup in two cans of different sizes. For the larger can, both the diameter and the height have been increased by 15%.

By what percentage does the volume increase from the smaller can to the larger can? Round your answer to the nearest percent. ​

Solution

the volume of a cylinder is given by:

$V=\pi r^2h$

We know that the diameter=radius and the height are increased by 15% so then the new volume can be calculated on this way:

$V=\pi(1.15r)^2\cdot(1.15h)=1.15^2\cdot1.15\cdot\pi\cdot r^2\cdot h=1.52\pi r^2h$

And the new volume would increase about 52%