Chapter 12.4, Problem 41PPS

a.

To determine

Toinvestigate : Right and oblique cylinders.

Explanation of Solution

Given information : To draw right cylinder and oblique cylinder with a height of $10m$ and diameter of $6m$ .

Graph :

Fig. 1: Right Cylinder

Fig. 2: Oblique Cylinder

Interpretation : The sides of the oblique cylinder are not perpendicular to the base. While the sides of the right cylinder are perpendicular to the base.

b.

To determine

Tofind: If the volume of the square prism is less than, greater than, or equal to the volume of the cylinder.

Explanation of Solution

Given information : Square prism with a height of $10m$ and base edge of $6m$ . And, the cylinder with a height of $10m$ and diameter of $6m$ .

Formula used : The volume of the square prism is $V_p=a^{2}h$ . And, the volume of a cylinder is $V_c=\frac{\pi d^{2}h}{4}$ .

Calculation : Calculate the volume of each shape.

$\begin{array}{l}{V}_p=a^{2}h\\ =6^2\times 10\\ V_p=360m^2\end{array}$

$\begin{array}{l}{V}_c=\frac{\pi d^{2}h}{4}\\ =\frac{\pi \times 6^2\times 10}{4}\\ V_c=282.7m^2\end{array}$

Interpretation : The volume of the square prism is greater than the volume of the cylinder.

c.

To determine

To explain: the change which affects the volume of the cylinder more: multiplying the height by x or multiplying the radius by x .

Explanation of Solution

The volume of a cylinder is $V_c=\pi r^{2}h$ .

If we multiply by height by x , the volume becomes $V_1=\pi r^{2}xh$

And, if we multiply the radius by x, the volume becomes $V_2=\pi {\left(xr\right)}^{2}h=\pi x^2{r}^{2}h$

We can see $V_2=x{V}_1$ .

So, the volume of the cylinder will be more, if we multiply the radius by x .