What is the cost of lighting a 500-watt outdoor light for 8 hours, if electricity costs 7.5 cents per kilowatt-hour?
The Correct Answer and Explanation is:
To calculate the cost of lighting a 500-watt outdoor light for 8 hours, we need to follow these steps:
Step 1: Convert watts to kilowatts
Electricity is typically billed in kilowatt-hours (kWh), so we must convert the wattage of the light into kilowatts.
1 kilowatt (kW) = 1,000 watts (W)
To convert 500 watts to kilowatts, divide by 1,000:
[
500 \, \text{watts} = \frac{500}{1000} = 0.5 \, \text{kilowatts}
]
Step 2: Calculate the total kilowatt-hours used
Next, we calculate the total amount of electricity consumed over the 8-hour period. Since the light uses 0.5 kilowatts and is on for 8 hours, the total energy consumption is:
[
\text{Energy consumed} = 0.5 \, \text{kW} \times 8 \, \text{hours} = 4 \, \text{kWh}
]
Step 3: Calculate the cost
Now that we know the light uses 4 kWh, we can calculate the cost of running the light for 8 hours. The cost of electricity is given as 7.5 cents per kilowatt-hour.
To find the total cost, multiply the total kilowatt-hours used by the cost per kilowatt-hour:
[
\text{Cost} = 4 \, \text{kWh} \times 7.5 \, \text{cents/kWh} = 30 \, \text{cents}
]
Final Answer:
The cost of lighting the 500-watt outdoor light for 8 hours is 30 cents.
Explanation:
Electricity bills are based on the amount of energy consumed, measured in kilowatt-hours (kWh). Since 1 kilowatt equals 1,000 watts, we first convert the wattage of the light to kilowatts to make the calculation consistent with billing units. The energy consumption is found by multiplying the power consumption (in kilowatts) by the time it is used (in hours). Finally, multiplying the energy consumption (in kWh) by the cost per kWh gives the total cost of using the light. By following these steps, we determine the total cost as 30 cents for 8 hours of use.