Chapter 1.1, Problem 42PPS

(a)

To determine

To draw two cylinders of different sizes.

Explanation of Solution

Given:

The volume of a cylinder can be found using the formula $v=\pi r^{2}h,$ in which $v=$ volume, $r=$ radius, and $h=$ height.

Calculation:

The two cylinders of different sizes are given as below;

The height of the cylinder A is $h_1$ and the radius is $r_1$ , the height of the cylinder B is $h_2$ and the radius is $r_2$ .

(b)

To determine

To use a ruler to measure the radius and height of each cylinder.

Explanation of Solution

Given:

The volume of a cylinder can be found using the formula $v=\pi r^{2}h,$ in which $v=$ volume, $r=$ radius, and $h=$ height.

Calculation:

The radius of cylinder is calculated by measuring the distance from the center of the circle of the cylinder to its end. The radius of cylinder A is $3.2$ cm and radius of cylinder B is $4.5$ cm.

The height of the cylinder is measured from the center of the circle of the cylinder to the center of the other circle. The height of the cylinder A is $7.5$ cm and the height of the cylinder B is $11.2$ cm.

Record of measures in tabular format;

(c)

To determine

To write a verbal expression for the difference in volume of the two cylinders

Explanation of Solution

Given:

The volume of a cylinder can be found using the formula $v=\pi r^{2}h,$ in which $v=$ volume, $r=$ radius, and $h=$ height.

Calculation:

Difference in two cylinders; Cylinder B is more elongated than cylinder as shown in figure. The difference in the radius of the cylinder is slighter but the height of the cylinder B is more than the height of the cylinder A. so, the volume of the cylinder B is approximately more than times the volume of the cylinder A.

(d)

To determine

To write and solve an algebraic expression for the difference in volume of the two cylinders.

Answer to Problem 42PPS

  $157.15{\text{ cm}}^3$

Explanation of Solution

Given:

The volume of a cylinder can be found using the formula $v=\pi r^{2}h,$ in which $v=$ volume, $r=$ radius, and $h=$ height.

Calculation:

Algebraic expression difference in volume is given as below;

Difference in the volume of cylinder $=$ Volume of Cylinder B $-$ Volume of Cylinder A

  $\begin{array}{l}=237.6-80.45\\ =157.15{\text{ cm}}^3\end{array}$