Jared is a farmer from Washington State. He is getting ready for a severe winter by cutting up wood into half-logs. To heat his house, he needs 154 dm³ of wood every day. The profi... Jared is a farmer from Washington State. He is getting ready for a severe winter by cutting up wood into half-logs. To heat his house, he needs 154 dm³ of wood every day. The profile of a half-log and its dimensions are described below. How many half-logs will Jared need to heat his house for ninety days?
Understand the Problem
The question is asking how many half-logs Jared needs to heat his house for ninety days, given the volume of wood he needs and the dimensions of a half-log. The first step will be to calculate the volume of a single half-log and then determine how many such volumes are needed for the total amount of wood required.
Answer
Jared needs approximately 495 half-logs to heat his house for ninety days.
Answer for screen readers
Jared needs approximately 495 half-logs to heat his house for ninety days.
Steps to Solve
- Calculate daily wood requirement for ninety days
To find the total amount of wood Jared needs for ninety days, multiply the daily requirement by ninety.
$$ \text{Total volume} = 154 \text{ dm}^3 \times 90 = 13860 \text{ dm}^3 $$
- Calculate the volume of a single half-log
The volume of a half-log can be calculated using the formula for the volume of a rectangular prism, as the half-log is shaped like a rectangular prism. Given the dimensions of the half-log (70 cm length, 20 cm width, and we assume the height is the same as the width for the half-log's profile):
Convert the dimensions from cm to dm:
- Length = 70 cm = 7 dm
- Width = 20 cm = 2 dm
Now, use the formula:
$$ \text{Volume of half-log} = \text{Length} \times \text{Width} \times \text{Height} = 7 \text{ dm} \times 2 \text{ dm} \times 2 \text{ dm} = 28 \text{ dm}^3 $$
- Determine the number of half-logs needed
To find out how many half-logs Jared needs, divide the total volume required by the volume of a single half-log:
$$ \text{Number of half-logs} = \frac{\text{Total volume}}{\text{Volume of half-log}} = \frac{13860 \text{ dm}^3}{28 \text{ dm}^3} \approx 495 $$
Jared needs approximately 495 half-logs to heat his house for ninety days.
More Information
Jared requires 154 dm³ of wood daily, which totals 13860 dm³ over ninety days. The volume of a half-log is 28 dm³, leading to the conclusion that he needs 495 half-logs.
Tips
- Forgetting to convert units: If dimensions are not converted correctly to the same unit system, it will lead to incorrect volume calculations. Always ensure that you are using the same units throughout the calculations.
- Miscalculating the volume by not using the correct formula for shapes. Ensure to use the correct formula based on the shape of the object in question.
AI-generated content may contain errors. Please verify critical information
