Chapter 12.6, Problem 29STP

(a)

To determine

To find: The volume of the smallest canister.

Answer to Problem 29STP

The volume of the smallest canister is $77.8{\text{in}}^{\text{3}}$ .

Explanation of Solution

Given Information:

The height of the smallest canister is 11 inches and radius is $1.5$ inches.

Calculation:

Write the expression for the volume of the canister.

  $V=\pi r^{2}h$

Where,

• $r$ is the radius of the canister.
• $h$ is the height of the canister.

Substitute the values in the above equation.

  $\begin{array}{c}V=\pi {\left(1.5\right)}^{2}11\\ \approx 77.8{\text{in}}^{\text{3}}\end{array}$

Conclusion:

Therefore, the volume of the smallest canister is $77.8{\text{in}}^{\text{3}}$ .

(b)

To determine

To find: The volume of the medium canister.

Answer to Problem 29STP

The volume of the medium canister is $700.7{\text{in}}^{\text{3}}$ .

Explanation of Solution

Given Information:

The height of the medium canister is 11 inches and radius is tripled in comparison to the smallest canister.

Calculation:

Calculate the radius of the medium canister.

  $\begin{array}{c}{r}_1=3\times 1.5\\ =4.5\text{inches}\end{array}$

Write the expression for the volume of the medium canister.

  $V=\pi r_1{}^{2}h$

Where,

• $r_1$ is the radius of the medium canister.
• $h$ is the height of the canister.

Substitute the values in the above equation.

  $\begin{array}{c}V=\pi {\left(4.5\right)}^{2}11\\ \approx 700.7{\text{in}}^{\text{3}}\end{array}$

Conclusion:

Therefore, the volume of the medium canister is $700.7{\text{in}}^{\text{3}}$ .