Question
a quart of paint will cover 100 sq ft how many quarts will be needed to paint a room with the length of 12ft a width of 10ft and a height of 8ft
Answers
GPT-4o mini
To determine how many quarts of paint are needed to paint the room, we first need to calculate the total surface area that will be painted. In a room, this typically includes the walls and possibly the ceiling, depending on the requirements.
1. **Calculate the area of the walls:**
There are 4 walls in the room:
- Two walls will have dimensions of 12 ft (length) and 8 ft (height).
- Two walls will have dimensions of 10 ft (width) and 8 ft (height).
Area of two 12 ft walls:
\[
2 \times (12 \text{ ft} \times 8 \text{ ft}) = 2 \times 96 \text{ sq ft} = 192 \text{ sq ft}
\]
Area of two 10 ft walls:
\[
2 \times (10 \text{ ft} \times 8 \text{ ft}) = 2 \times 80 \text{ sq ft} = 160 \text{ sq ft}
\]
**Total wall area:**
\[
192 \text{ sq ft} + 160 \text{ sq ft} = 352 \text{ sq ft}
\]
2. **Calculate the area of the ceiling:**
The area of the ceiling is given by the length times the width:
\[
12 \text{ ft} \times 10 \text{ ft} = 120 \text{ sq ft}
\]
3. **Total surface area to be painted:**
\[
352 \text{ sq ft} \text{ (walls)} + 120 \text{ sq ft} \text{ (ceiling)} = 472 \text{ sq ft}
\]
4. **Determine how many quarts of paint are needed:**
Since 1 quart of paint covers 100 sq ft, we can calculate the number of quarts needed as follows:
\[
\text{Quarts needed} = \frac{472 \text{ sq ft}}{100 \text{ sq ft/quart}} = 4.72 \text{ quarts}
\]
Since you cannot purchase a fraction of a quart, you will need to round up to the next whole number.
Thus, you will need **5 quarts of paint** to cover the room.
1. **Calculate the area of the walls:**
There are 4 walls in the room:
- Two walls will have dimensions of 12 ft (length) and 8 ft (height).
- Two walls will have dimensions of 10 ft (width) and 8 ft (height).
Area of two 12 ft walls:
\[
2 \times (12 \text{ ft} \times 8 \text{ ft}) = 2 \times 96 \text{ sq ft} = 192 \text{ sq ft}
\]
Area of two 10 ft walls:
\[
2 \times (10 \text{ ft} \times 8 \text{ ft}) = 2 \times 80 \text{ sq ft} = 160 \text{ sq ft}
\]
**Total wall area:**
\[
192 \text{ sq ft} + 160 \text{ sq ft} = 352 \text{ sq ft}
\]
2. **Calculate the area of the ceiling:**
The area of the ceiling is given by the length times the width:
\[
12 \text{ ft} \times 10 \text{ ft} = 120 \text{ sq ft}
\]
3. **Total surface area to be painted:**
\[
352 \text{ sq ft} \text{ (walls)} + 120 \text{ sq ft} \text{ (ceiling)} = 472 \text{ sq ft}
\]
4. **Determine how many quarts of paint are needed:**
Since 1 quart of paint covers 100 sq ft, we can calculate the number of quarts needed as follows:
\[
\text{Quarts needed} = \frac{472 \text{ sq ft}}{100 \text{ sq ft/quart}} = 4.72 \text{ quarts}
\]
Since you cannot purchase a fraction of a quart, you will need to round up to the next whole number.
Thus, you will need **5 quarts of paint** to cover the room.