Question

a can company makes a cylindrical can that has a radius of 6 cm and a height of 10 cm. one of the company’s clients needs a cylindrical can that has the same volume but is 15 cm tall. what must the new radius be to meet the client’s need? round to the nearest tenth of a centimeter
○ 2.7 cm
○ 4.9 cm
○ 7.3 cm
○ 24.0 cm

Explanation:

Step1: Find original can volume

Volume formula: $V = \pi r^2 h$
$V = \pi \times 6^2 \times 10 = 360\pi$

Step2: Set up new volume equation

New height $h_{new}=15$, let $r_{new}=r$:
$360\pi = \pi r^2 \times 15$

Step3: Solve for $r^2$

Cancel $\pi$, divide by 15:
$r^2 = \frac{360}{15} = 24$

Step4: Calculate new radius

Take square root, round to tenth:
$r = \sqrt{24} \approx 4.9$

Answer:

B. 4.9 cm