Questions: What are the lateral surface area and total surface area of a cylindrical oil storage tank that has a 56-ft diameter and 13-ft height? L.A. = 2πrh S.A. = 2πrh + πr^2 + πr^2 The lateral surface area of the cylindrical oil storage tank is ft^2. (Round to one decimal place as needed.) The total surface area of the cylindrical oil storage tank is ft^2. (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest tenth as needed.)

What are the lateral surface area and total surface area of a cylindrical oil storage tank that has a 56-ft diameter and 13-ft height? L.A. = 2πrh S.A. = 2πrh + πr^2 + πr^2 The lateral surface area of the cylindrical oil storage tank is ft^2. (Round to one decimal place as needed.) The total surface area of the cylindrical oil storage tank is ft^2. (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest tenth as needed.)
Transcript text: What are the lateral surface area and total surface area of a cylindrical oil storage tank that has a 56 -ft diameter and 13 -ft height? \[ \begin{array}{l} \text { L.A. }=2 \pi r h \\ \text { S.A. }=2 \pi r h+\pi r^{2}+\pi r^{2} \end{array} \] The lateral surface area of the cylindrical oil storage tank is $\square$ $\mathrm{ft}^{2}$. (Round to one decimal place as needed.) The total surface area of the cylindrical oil storage tank is $\square \mathrm{ft}^{2}$. (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest tenth as needed.)
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Solution

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Solution Steps

To find the lateral surface area and total surface area of a cylindrical oil storage tank, we need to use the formulas for lateral area (L.A.) and surface area (S.A.). The lateral surface area is calculated using the formula \( L.A. = 2 \pi r h \), where \( r \) is the radius and \( h \) is the height of the cylinder. The total surface area is calculated using the formula \( S.A. = 2 \pi r h + 2 \pi r^2 \), which includes the lateral area plus the area of the two circular ends. Given the diameter, we first find the radius by dividing the diameter by 2.

Step 1: Calculate the Radius

Given the diameter \( d = 56 \, \text{ft} \), the radius \( r \) is calculated as: \[ r = \frac{d}{2} = \frac{56}{2} = 28.0 \, \text{ft} \]

Step 2: Calculate the Lateral Surface Area

Using the formula for lateral surface area \( L.A. = 2 \pi r h \): \[ L.A. = 2 \pi (28.0) (13) \approx 2287.1 \, \text{ft}^2 \]

Step 3: Calculate the Total Surface Area

Using the formula for total surface area \( S.A. = 2 \pi r h + 2 \pi r^2 \): \[ S.A. = 2 \pi (28.0)(13) + 2 \pi (28.0)^2 \approx 7213.1 \, \text{ft}^2 \]

Final Answer

The lateral surface area of the cylindrical oil storage tank is \( \boxed{2287.1 \, \text{ft}^2} \) and the total surface area is \( \boxed{7213.1 \, \text{ft}^2} \).

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