Question
A furnace is designed to heat 15 comma 000 cubic feet. Will this furnace be adequate for a 1100-square-foot house with a 10-foot ceiling?
Answers
GPT-4o mini
To determine if the furnace will be adequate for your house, you need to calculate the total volume of the house and then compare that with the heating capacity of the furnace.
1. **Calculate the volume of the house:**
- The formula for volume is:
\[
\text{Volume} = \text{Area} \times \text{Height}
\]
- Given the area of the house is 1100 square feet and the height of the ceiling is 10 feet, you can calculate the volume as follows:
\[
\text{Volume} = 1100 \, \text{sq ft} \times 10 \, \text{ft} = 11,000 \, \text{cubic feet}
\]
2. **Compare the house volume with the furnace capacity:**
- The furnace is designed to heat 15,000 cubic feet, and the calculated volume of the house is 11,000 cubic feet.
Since 11,000 cubic feet is less than 15,000 cubic feet, the furnace will be adequate to heat the house.
**Conclusion: Yes, the furnace will be adequate for a 1100-square-foot house with a 10-foot ceiling.**
1. **Calculate the volume of the house:**
- The formula for volume is:
\[
\text{Volume} = \text{Area} \times \text{Height}
\]
- Given the area of the house is 1100 square feet and the height of the ceiling is 10 feet, you can calculate the volume as follows:
\[
\text{Volume} = 1100 \, \text{sq ft} \times 10 \, \text{ft} = 11,000 \, \text{cubic feet}
\]
2. **Compare the house volume with the furnace capacity:**
- The furnace is designed to heat 15,000 cubic feet, and the calculated volume of the house is 11,000 cubic feet.
Since 11,000 cubic feet is less than 15,000 cubic feet, the furnace will be adequate to heat the house.
**Conclusion: Yes, the furnace will be adequate for a 1100-square-foot house with a 10-foot ceiling.**