Question

find the surface area of a cylinder that has a radius of 12.1 ft and a height of 20.5 ft. use 3.14 for pi and round your answer to the nearest hundredth. do not include a unit of measure with your response. 11 formula 0.5 points find the volume of a box that has a length of 28.3 cm, a width of 11 cm, and a height of 11.1 cm. round your answer to the nearest hundredth, but do not include \cm³\ with your response.

Explanation:

Step1: Recall surface - area formula for cylinder

The surface - area formula of a cylinder is $S = 2\pi r^{2}+2\pi rh$, where $r$ is the radius and $h$ is the height.

Step2: Substitute given values

Given $r = 12.1$, $h = 20.5$, and $\pi=3.14$. First, calculate $2\pi r^{2}$:
$2\times3.14\times(12.1)^{2}=2\times3.14\times146.41 = 919.5452$.
Then, calculate $2\pi rh$:
$2\times3.14\times12.1\times20.5=2\times3.14\times248.05 = 1557.566$.

Step3: Add the two results

$S=919.5452 + 1557.566=2477.1112\approx2477.11$.

Step4: Recall volume formula for box

The volume formula of a box (rectangular prism) is $V=l\times w\times h$, where $l$ is the length, $w$ is the width, and $h$ is the height.

Step5: Substitute given values

Given $l = 28.3$, $w = 11$, and $h = 11.1$. Then $V=28.3\times11\times11.1 = 28.3\times122.1=3455.43$.

Answer:

2477.11
3455.43