Chapter 12.4, Problem 25PPS

To determine

To find:

The height of the larger can.

Answer to Problem 25PPS

The height of the larger can is $35.1\text{ cm}$ .

Explanation of Solution

Given information:

A cylindrical can of baked potato chips has a height of $27$ centimeters and a radius $4$ centimeters.

Calculation:

The smaller can has a height of $27$ centimeters and a radius $4$ centimeters.

Volume of the smaller can is:

  $\begin{array}{c}V=\pi {\left(4\right)}^2\left(27\right)\\ =432\pi \end{array}$

The volume of the new can is $130\%$ of the smaller can, with the same radius.

Assume that the height of the new can is $h\text{ cm}$ .

  $\begin{array}{c}130\%of432\pi =\pi {\left(4\right)}^2\left(h\right)\\ 1.3\cdot 432\pi =16\pi h\\ h=\frac{1.3\left(432\right)\pi }{16\pi }\\ =35.1\end{array}$

Hence, the height of the larger can is $35.1\text{ cm}$ .