Question

a company is designing a soup can that is in the shape of a right circular cylinder. the height of the can will be 3 times the radius of the can. the volume of the can will be 350 cubic centimeters. which measurement, in centimeters, is closest to the radius of the soup can? a. 2.3 cm b. 3.3 cm c. 6.9 cm d. 9.9 cm

Explanation:

Step1: Recall volume formula for cylinder

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

Step2: Express height in terms of radius

Given that $h = 3r$. Substitute $h = 3r$ into the volume formula: $V=\pi r^{2}(3r)=3\pi r^{3}$.

Step3: Solve for radius

We know that $V = 350$ cubic centimeters. So, $3\pi r^{3}=350$. Then $r^{3}=\frac{350}{3\pi}$.
Taking $\pi\approx3.14$, we have $r^{3}=\frac{350}{3\times3.14}=\frac{350}{9.42}\approx37.15$.
Taking the cube - root of both sides, $r=\sqrt[3]{37.15}\approx3.3$ cm.

Answer:

B. 3.3 cm