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POS The radius of a cylindrical box of oatmeal is 5 centimeters. The height of the box is 18 centimeters. 5 cm 18 cm QATMEAL Which measurement is closest to the total surface area of the oatmeal box in square centimeters? A 597 cm2 B 361 cm? C 314 cm? D 723 cm?

POS The radius of a cylindrical box of oatmeal is 5 centimeters The height of the box is 18 centimeters 5 cm 18 cm QATMEAL Which measurement is closest to the t class=

Respuesta :

[tex]723cm^2[/tex]

Explanation

Step 1

to find the area, imagine the unfolded cylindrical box

Let

length=18 cm

width=2*pi*radius

radius= 5 cm

[tex]\begin{gathered} \text{width}=2\cdot\pi\cdot5\text{ cm} \\ \text{width}=10\cdot\pi\cdot\text{cm} \\ \text{width}=31.4\text{ cm} \end{gathered}[/tex]

Step 2

now, the total area would be

[tex]\begin{gathered} \text{total area= area of the rectangle+twice area of the circle} \\ \text{replacing} \\ \text{total area=(length}\cdot widht9+2(\pi\cdot radius^2) \\ \text{total area=(18 cm}\cdot31.4\text{ cm)+2(3.14}\cdot25cm^2) \\ \text{total area=565.2 cm}^2+157.07cm^2 \\ \text{total area=722.27 cm}^2 \\ \text{rounded} \\ 723cm^2 \end{gathered}[/tex]

I hope this helps you

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