Question

which of the following dimensions would result in the largest volume for a cylinder?
a. r = 2 cm, h = 10 cm
b. r = 3 cm, h = 6 cm
c. r = 5 cm, h = 4 cm
d. r = 4 cm, h = 5 cm
what is the approximate value of π?
a. 3.41
b. 3.0
c. 3.14
d. 3.5

Explanation:

Step1: Recall volume formula

The volume formula for a cylinder is $V=\pi r^{2}h$.

Step2: Calculate volume for option a

For $r = 2$ cm and $h=10$ cm, $V_a=\pi\times(2)^{2}\times10=\pi\times4\times 10 = 40\pi$ $cm^{3}$.

Step3: Calculate volume for option b

For $r = 3$ cm and $h = 6$ cm, $V_b=\pi\times(3)^{2}\times6=\pi\times9\times6=54\pi$ $cm^{3}$.

Step4: Calculate volume for option c

For $r = 5$ cm and $h = 4$ cm, $V_c=\pi\times(5)^{2}\times4=\pi\times25\times4 = 100\pi$ $cm^{3}$.

Step5: Calculate volume for option d

For $r = 4$ cm and $h = 5$ cm, $V_d=\pi\times(4)^{2}\times5=\pi\times16\times5=80\pi$ $cm^{3}$.
Since $100\pi>80\pi > 54\pi>40\pi$, option c gives the largest volume.

The approximate value of $\pi$ is 3.14.

Answer:

1. C. $r = 5$ cm, $h = 4$ cm
2. C. 3.14