Chapter 12.8, Problem 15PPS

a.

To determine

To determine the scale factor of the cylinders.

Answer to Problem 15PPS

  $10:13$

Explanation of Solution

Given:

A small cylindrical can of tuna has a radius of 4 centimeters and a height of 3.8 centimeters.

A larger and similar can of tuna has a radius of $5.2$ centimeters.

Calculation:

A small cylindrical can of tuna has a radius of 4 centimeters and a larger and similar can of tuna has a radius of $5.2$ centimeters.

From the information, the scale factor of their radii is,

  $\Rightarrow 4:5.2$

Multiplying both the part of the ratio with $5$ to remove the point and make it divisible,

  $\Rightarrow 4\times 5:5.2\times 5$

  $\Rightarrow 20:26$

Now dividing the common part,

  $\Rightarrow 10:13$

Now finding the height of the larger can, considering the height as $h$ .

The ratio of radii is equal to ratio of the height,

  $\Rightarrow \frac{10}{13}=\frac{3.8}{h}$

Cross multiplying,

  $\Rightarrow 10h=13\times 3.8$

  $\Rightarrow h=\frac{13\times 3.8}{10}$

  $\Rightarrow h=4.94$

Conclusion:

Therefore, the scale factor of the cylinders is $10:13$ .

b.

To determine

To determine the volume of the larger can.

Answer to Problem 15PPS

  $419.6{\text{ centimeter}}^3$

Explanation of Solution

Given:

A small cylindrical can of tuna has a radius of 4 centimeters and a height of 3.8 centimeters.

A larger and similar can of tuna has a radius of $5.2$ centimeters.

Formula used:

Volume of the cylinder $=\pi r^{2}h$

  $\left[r=\text{radius and }h=\text{height}\right]$

Calculation:

From the previous part the value of height is $h=\mathrm{4.94.}$

  $\Rightarrow$ Volume of the cylinder $=\pi r^{2}h$

  $\Rightarrow \text{The volume of the larger can}=\pi \times {(5.2)}^2\times 4.94$

  $=419.646{\text{ centimeter}}^3$

Rounding off to nearest tenth,

  $\Rightarrow \text{The volume of the larger can}$

  $\approx 419.6{\text{ centimeter}}^3$

Conclusion:

Therefore, the volume of the larger can is $\approx 419.6{\text{ centimeter}}^3$ .