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Answer the questions below to find the total surface area of the can.

Answer the questions below to find the total surface area of the can.-example-1

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Answer:


\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}

Explanation:

We can find the Surface Area of the can by adding the areas of each of its parts:


SA = 2( A_{\text{base}}) + A_\text{side}

First, we can calculate the area of the circular base:


A_{\text{circle}} = \pi r^2


A_{\text{base}} = \pi (0.75 \text{ in})^2


A_{\text{base}} = 0.5625\pi \text{ in}^2

Next, we can calculate the area of the rectangular side:


A_\text{rect} = l \cdot w


A_\text{side} = (4\text{ in}) \cdot C_\text{base}

Since the width of the side is the circumference of the base, we need to calculate that first.


C_\text{circle} = 2 \pi r


C_\text{base} = 2 \pi (0.75 \text{ in})


C_\text{base} = 1.5 \pi \text{ in}

Now, we can plug that back into the equation for the area of the side:


A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})


A_\text{side} = 6\pi \text{ in}^2

Finally, we can solve for the surface area of the can by adding the area of each of its parts.


SA = 2( A_{\text{base}}) + A_\text{side}


SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2


\boxed{SA = 7.125\pi \text{ in}^2}


\boxed{SA \approx 22.4 \text{ in}^2}

User Lazarus Lazaridis
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