Let's address the relevant question step by step.
Problem 10: A cylindrical tank whose diameter is 140 cm has a height of 75 cm. How many liters of water can it hold when full?
To solve this problem, follow these steps:
1. Determine the radius of the cylinder:
The diameter of the tank is 140 cm, so the radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[
r = \frac{140}{2} \text{ cm}
\][/tex]
[tex]\[
r = 70 \text{ cm}
\][/tex]
2. Determine the height of the cylinder:
The height [tex]\( h \)[/tex] of the tank is given to be 75 cm.
3. Calculate the volume of the cylinder in cubic centimeters:
The formula for the volume [tex]\( V \)[/tex] of a cylinder is:
[tex]\[
V = \pi r^2 h
\][/tex]
Substituting the values we have:
[tex]\[
V = \pi (70)^2 (75) \text{ cubic centimeters}
\][/tex]
4. Find the volume in cubic centimeters:
Using the values for [tex]\(\pi \approx 3.141592653589793\)[/tex], [tex]\( r = 70 \text{ cm} \)[/tex], and [tex]\( h = 75 \text{ cm} \)[/tex]:
[tex]\[
V \approx 3.141592653589793 \times 70^2 \times 75 \text{ cubic centimeters}
\][/tex]
[tex]\[
V \approx 3.141592653589793 \times 4900 \times 75 \text{ cubic centimeters}
\][/tex]
[tex]\[
V \approx 1154535.300194249 \text{ cubic centimeters}
\][/tex]
5. Convert the volume to liters:
Knowing that 1 liter = 1000 cubic centimeters, we can convert the volume from cubic centimeters to liters by dividing by 1000:
[tex]\[
\text{Volume in liters} = \frac{1154535.300194249 \text{ cubic centimeters}}{1000}
\][/tex]
[tex]\[
\text{Volume in liters} \approx 1154.535300194249 \text{ liters}
\][/tex]
Answer:
The cylindrical tank can hold approximately 1154.54 liters of water when full.
