Question

What is the lateral and total surface area for the object shown below

Answer 1

- Lateral Surface Area (L) = 109.56 square feet

- Total Surface Area (S) = 186.93 square feet

SOLUTION

Problem Statement

The question asks us to find the Lateral and Total Surface Area for a cylinder of diameter 7ft and height of 5ft.

Method

- The Total Surface Area and Lateral Area of a cylinder can be gotten using the formulas given below:

`\begin{gathered} \text{Lateral Area of a Cylinder:} \\ L=2\pi rh_{} \\ \\ \text{Total Surface Area of a Cylinder:} \\ S=2\pi r^2+2\pi rh \\ \\ \text{where,} \\ r=\text{radius of the Cylinder} \\ h=\text{height of the Cylinder} \end{gathered}`

- The formula above gives us the formulas for the Lateral Area and the Total Surface Area in terms of the radius (r). We are given the diameter of the Cylinder as 7ft. This means we need to find the radius of the Cylinder from the diameter given.

`\begin{gathered} \text{radius}=\frac{\text{ Diameter}}{\text{2}} \\ \\ r=(7)/(2)ft \end{gathered}`

- Now, we are all set to calculate the Lateral Area and the Total Surface Area of the Cylinder.

Implementation

Lateral Surface Area:

`\begin{gathered} L=2\pi rh \\ r=(7)/(2),h=5 \\ \\ \therefore L=2*\pi*(7)/(2)*5 \\ \\ L=35\pi\approx109.56ft^2 \end{gathered}`

Total Surface Area:

`\begin{gathered} S=2\pi rh+2\pi r^2 \\ r=(7)/(2),h=5 \\ \\ \therefore S=(2*\pi*(7)/(2)*5)+(2*\pi*(7)/(2)*(7)/(2)) \\ S=35\pi+(49\pi)/(2) \\ \\ \therefore S=(119\pi)/(2)\approx186.93ft^2 \end{gathered}`

Final Answer

The answers are:

- Lateral Surface Area (L) = 109.56 square feet

- Total Surface Area (S) = 186.93 square feet.