Question

the surface area of a right - circular cylinder is given by the polynomial 2πrh + 2πr², where h is the height, r is the radius of the base, and r and h are given in the same units. a beverage can has height 6.3 in. and radius 1.1 in. find the surface area of the can. (use a calculator with a π key or use 3.141592654 for π.) the surface area of the can is . (type an integer or a decimal. do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Identify the formula

The surface - area formula of a right - circular cylinder is $S = 2\pi rh+2\pi r^{2}$, where $h = 6.3$ in and $r = 1.1$ in.

Step2: Calculate the lateral - surface area ($2\pi rh$)

$2\pi rh=2\times\pi\times1.1\times6.3 = 13.86\pi$.

Step3: Calculate the area of the two bases ($2\pi r^{2}$)

$2\pi r^{2}=2\times\pi\times(1.1)^{2}=2\times\pi\times1.21 = 2.42\pi$.

Step4: Calculate the total surface area

$S=13.86\pi + 2.42\pi=16.28\pi$.
Using $\pi\approx3.141592654$, we have $S = 16.28\times3.141592654=51.14412831$.

Step5: Round the answer

Rounding to the nearest tenth, $S\approx51.1$.

Answer:

$51.1$