Question

a container for posters is shaped like a cylinder its dimensions are shown in the diagram3 1 over 4 as the height and 19 as the base.which measurement is closest to the total surface area in square inches494.80228.16182.8066.50

Answer 1

First, the measures we have are:

The diameter of the cylinder is:

we will call the diameter "d" for reference:

`d=3(1)/(2)\text{ in}=3.5in`

And we also have the height of the cylinder:

We will call this "h":

`h=19in`

The steps to find the surface area:

Step 1. The surface area of a cylinder is formed of two circles and one rectangle as shown in the following diagram:

Where h is the height, h=19in

r is the radius, defines as half of the diameter:

`\begin{gathered} r=(d)/(2) \\ r=(3.5in)/(2) \\ r=1.75in \end{gathered}`

And c is the circumference of the circle, defined as follows:

`c=d\pi`

Where pi is a constant: pi=3.1416

so we find the value of the circumference c:

`\begin{gathered} c=(3.5\text{ in)(3.1415)} \\ c=10.995in \end{gathered}`

Step 2. Calculate the area of the two circles of the area.

The formula to calculate the area of a circle is:

`A=\pi* r^2`

We substitute our values:

`\begin{gathered} A=3.1416*(1.75in)^2 \\ \end{gathered}`

And solving the operations:

`\begin{gathered} A=3.1416*3.0625in^2 \\ A=9.62in^2 \end{gathered}`

And we need to multiply this are by 2 because there are two identical circles:

`\begin{gathered} A=2*9.62in^2 \\ A=19.24in^2 \end{gathered}`

Step 3. Calculate the area of the rectangle.

To calculate that area we multiply the h by c:

`A=h* c`

Substituting our h and c values:

`\begin{gathered} A=19in*10.995in \\ A=208.905in^2 \end{gathered}`

Step 4. Add the area of the circles and the rectangle to find the total surface area:

`\begin{gathered} A_{\text{surface}}=19.24in^2+208.905in^2 \\ A_{\text{Surface}}=228.145in^2 \end{gathered}`

The closest value out of the options is: 228.16

Answer: 228.16