To estimate the length of time it will take to fill three-quarters of a bathtub given the provided dimensions and flow rate of the tap, please follow the detailed steps below:
1. Determine the volume of the bathtub:
The bathtub is modeled as a cuboid with the following dimensions:
- Length = 152 cm
- Width = 76 cm
- Height = 36 cm
The volume of the cuboid can be calculated using the formula for the volume of a rectangular prism (cuboid):
[tex]\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\][/tex]
Substituting the given values:
[tex]\[
\text{Volume} = 152 \, \text{cm} \times 76 \, \text{cm} \times 36 \, \text{cm} = 415,872 \, \text{cm}^3
\][/tex]
2. Convert the volume from cubic centimeters to liters:
We know that 1 cubic centimeter (cm³) is equivalent to 0.001 liters. Therefore, we can convert the volume from cubic centimeters to liters by multiplying by 0.001:
[tex]\[
\text{Volume in liters} = 415,872 \, \text{cm}^3 \times 0.001 = 415.872 \, \text{liters}
\][/tex]
3. Calculate the volume required to fill three-quarters of the bathtub:
To find three-quarters of the total volume, we multiply the total volume in liters by 0.75:
[tex]\[
\text{Volume of three-quarters} = 415.872 \, \text{liters} \times 0.75 = 311.904 \, \text{liters}
\][/tex]
4. Determine the flow rate of the tap:
The flow rate of the tap is given as 18 liters per minute.
5. Estimate the time needed to fill three-quarters of the bathtub:
To find the time required to fill the bathtub to three-quarters of its volume, we divide the volume of three-quarters by the flow rate of the tap:
[tex]\[
\text{Time required} = \frac{\text{Volume of three-quarters}}{\text{Flow rate}} = \frac{311.904 \, \text{liters}}{18 \, \text{liters per minute}} = 17.328 \, \text{minutes}
\][/tex]
Therefore, it will take approximately 17.328 minutes to fill three-quarters of the bathtub with water.
