Question

At the Olympics the winners stand on tiered pedestals.
Diagram shows,height of pedestal 3 is 7 inches,the height of pedestal 2 is 11 inches, and height of pedestal 3 is 15 inches. Assuming each pedestal is of equal width and depth ,find the total surface area of the stand.
The diagram shows the steps in 2,1 3 order left to right.
To left show 20 inches which is width and along the front shows a line left to right broken into 3 each labeled 20

Answer 1

To find the total surface area of the Olympic podium that consists of three tiered pedestals, we need to calculate the surface area of each pedestal individually and then sum them up. The podium has dimensions as follows:

1. **Pedestal 1**: Height = 7 inches
2. **Pedestal 2**: Height = 11 inches
3. **Pedestal 3**: Height = 15 inches
4. **Width and Depth**: 20 inches (common for all pedestals)

### Individual Surface Area Calculation:

**Step 1: Calculate the Surface Area of Each Pedestal.**

Each pedestal is a rectangular prism, and its surface area can be calculated using the formula:

\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]

Where:
- \( l \) is the length (depth),
- \( w \) is the width,
- \( h \) is the height.

Let's denote:
- Width \( w = 20 \) inches
- Depth \( l = 20 \) inches

#### 1. Surface Area of Pedestal 1 (7 inches)
\[
h_1 = 7 \text{ inches}
\]
\[
\text{Surface Area}_{1} = 2(20)(20) + 2(20)(7) + 2(20)(7)
\]
\[
= 800 + 280 + 280 = 1360 \text{ square inches}
\]

#### 2. Surface Area of Pedestal 2 (11 inches)
\[
h_2 = 11 \text{ inches}
\]
\[
\text{Surface Area}_{2} = 2(20)(20) + 2(20)(11) + 2(20)(11)
\]
\[
= 800 + 440 + 440 = 1680 \text{ square inches}
\]

#### 3. Surface Area of Pedestal 3 (15 inches)
\[
h_3 = 15 \text{ inches}
\]
\[
\text{Surface Area}_{3} = 2(20)(20) + 2(20)(15) + 2(20)(15)
\]
\[
= 800 + 600 + 600 = 2000 \text{ square inches}
\]

**Step 2: Calculate Total Surface Area.**

The total surface area of the three pedestals will be the sum of their individual surface areas:

\[
\text{Total Surface Area} = \text{Surface Area}_{1} + \text{Surface Area}_{2} + \text{Surface Area}_{3}
\]
\[
= 1360 + 1680 + 2000
\]
\[
= 5040 \text{ square inches}
\]

### Conclusion:
The total surface area of the tiered pedestal stand is **5040 square inches**.