Let's work through the two problems found in your document.

Problem 1:

How many gallons of paint are needed to paint a storage room 30m by 22m by 25m? The storage room has no windows, and 1 gallon can paint 400 sq. ft.

Step 1: Calculate the surface area of the storage room.

The storage room is a rectangular prism, so we calculate the area of each wall:

• Two walls of 30m by 25m
• Two walls of 22m by 25m
• The ceiling and floor (30m by 22m)

Convert meters to feet (1 meter = 3.28084 feet):

• 30m ≈ 98.43 ft
• 22m ≈ 72.18 ft
• 25m ≈ 82.02 ft

Now, calculate the area of each surface:

1. Two walls: $2 \times (98.43 \times 82.02)$
2. Two walls: $2 \times (72.18 \times 82.02)$
3. Ceiling and floor: $2 \times (98.43 \times 72.18)$

Step 2: Total surface area.

Add all the areas together: $A_{\text{total}} = 2 \times (98.43 \times 82.02) + 2 \times (72.18 \times 82.02) + 2 \times (98.43 \times 72.18)$

Step 3: Convert the total surface area to square feet.

Since 1 gallon covers 400 square feet, divide the total surface area by 400 to find how many gallons are needed.

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Problem 2:

Jed bought a generator that will run for 2 hours on a liter of gas. The gas tank on the generator is a rectangular prism with dimensions 20 cm by 15 cm by 10 cm. How long will the generator run if the tank is filled with gas?

Step 1: Calculate the volume of the gas tank.

The volume of a rectangular prism is $V = l \times w \times h$, where $l$, $w$, and $h$ are the dimensions of the tank.

Convert centimeters to liters (since 1 cubic centimeter = 0.001 liters): $V = 20 \, \text{cm} \times 15 \, \text{cm} \times 10 \, \text{cm} = 3000 \, \text{cm}^3 = 3 \, \text{liters}$

Step 2: Calculate the runtime.

If 1 liter of gas runs the generator for 2 hours, then 3 liters will run the generator for: $3 \times 2 = 6 \, \text{hours}$

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Let me know if you would like detailed calculations or clarifications on any of the steps!

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Follow-up questions:

1. How would the number of gallons of paint change if the room had a window?
2. What would happen if the dimensions of the storage room changed?
3. How do you convert from meters to feet or liters to cubic centimeters?
4. How would the runtime of the generator change if the tank size increased by 50%?
5. What is the impact of increasing the height of the storage room on the amount of paint needed?

Tip: Always check your units to ensure correct conversions, especially when switching between metric and imperial systems.