Chapter 7.1, Problem 61PPS

(a)

To determine

To find: The volume of her container.

Answer to Problem 61PPS

The volume of her container is $V=16\pi p^9$ .

Explanation of Solution

Given information:

The given function is the volume of a cylinder is $V=\pi r^{2}h$

Calculation:

Calculate the function.

  $\begin{array}{c}V=\pi {\left(2p^3\right)}^2\left(4p^3\right)\\ =\pi \left({\left(2\right)}^2{p}^{3*2}\right)\left(4p^3\right)\\ =\pi \left(4p^6\right)\left(4p^3\right)\\ =\left(4*4\right)\pi p^{6+3}\\ =16\pi p^9\end{array}$

Therefore, the volume of her container $V=16\pi p^9$ .

(b)

To determine

To find: The table volume for five possible radius width and height if the volume.

Answer to Problem 61PPS

The table volume for five possible radius width and height if the volume is shown in table (1) .

Explanation of Solution

Given information:

The given function is the volume of a cylinder is $V=\pi r^{2}h$

Calculation:

Consider the function the table of five possible measures for the radius and height of a cylinder is shown in the figure (1).

  

Table (1)

Therefore, the table volume for five possible radius width and height if the volume is shown in table (1) .

(c)

To determine

To find: The volume of Aiko’s container if the height is doubled.

Answer to Problem 61PPS

The volume of Aiko’s container if the height is doubled $V=32\pi p^9$ .

Explanation of Solution

Given information:

The given function is the volume of a cylinder is $V=\pi r^{2}h$

Calculation:

Calculate the function.

  $\begin{array}{c}V=\pi {\left(2p^3\right)}^2\left(8p^3\right)\\ =\pi \left({\left(2\right)}^2{p}^{3*2}\right)\left(4p^3\right)\\ =\pi \left(4p^6\right)\left(8p^3\right)\\ =\left(4*8\right)\pi p^{6+3}\\ =32\pi p^9\end{array}$

Therefore, the volume of Aiko’s container if the height is doubled $V=32\pi p^9$ .