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Answer :
Sure, let's solve this problem step by step:
1. Calculate the volume of the rectangular tank:
The dimensions of the rectangular tank are 27 cm (length), 20 cm (width), and 37 cm (height). To find the total volume of the tank in cubic centimeters (cm³), use the formula:
[tex]\[
\text{Volume of rectangular tank} = \text{length} \times \text{width} \times \text{height} = 27 \times 20 \times 37 = 19980 \text{ cm}^3
\][/tex]
2. Determine the initial volume of water in the rectangular tank:
The tank is initially filled to [tex]\(\frac{1}{2}\)[/tex] of its total volume. Thus, the volume of the water is:
[tex]\[
\text{Initial volume of water} = 19980 \times \frac{1}{2} = 9990 \text{ cm}^3
\][/tex]
3. Calculate the volume of the cubic tank:
The cubic tank has an edge length of 16 cm. The formula for the volume of a cube is:
[tex]\[
\text{Volume of cubic tank} = \text{edge}^3 = 16^3 = 4096 \text{ cm}^3
\][/tex]
4. Find the volume of water required to fill [tex]\(\frac{3}{4}\)[/tex] of the cubic tank:
The cubic tank is filled to [tex]\(\frac{3}{4}\)[/tex] of its volume. Therefore, the volume of water needed is:
[tex]\[
\text{Volume of water in cubic tank} = 4096 \times \frac{3}{4} = 3072 \text{ cm}^3
\][/tex]
5. Determine the volume of water remaining in the rectangular tank:
The water poured into the cubic tank from the rectangular tank reduces the water in the rectangular tank. So, the remaining volume of water is the initial volume minus the volume transferred:
[tex]\[
\text{Remaining volume of water} = 9990 - 3072 = 6918 \text{ cm}^3
\][/tex]
6. Convert the remaining volume to liters:
Since [tex]\(1 \text{ liter} = 1000 \text{ cm}^3\)[/tex], we convert the remaining volume to liters:
[tex]\[
\text{Remaining volume in liters} = \frac{6918}{1000} = 6.918 \text{ liters}
\][/tex]
7. Round the answer:
Finally, rounding the volume to one decimal place gives approximately 6.9 liters.
So, the remaining water in the rectangular tank is approximately 6.9 liters.
1. Calculate the volume of the rectangular tank:
The dimensions of the rectangular tank are 27 cm (length), 20 cm (width), and 37 cm (height). To find the total volume of the tank in cubic centimeters (cm³), use the formula:
[tex]\[
\text{Volume of rectangular tank} = \text{length} \times \text{width} \times \text{height} = 27 \times 20 \times 37 = 19980 \text{ cm}^3
\][/tex]
2. Determine the initial volume of water in the rectangular tank:
The tank is initially filled to [tex]\(\frac{1}{2}\)[/tex] of its total volume. Thus, the volume of the water is:
[tex]\[
\text{Initial volume of water} = 19980 \times \frac{1}{2} = 9990 \text{ cm}^3
\][/tex]
3. Calculate the volume of the cubic tank:
The cubic tank has an edge length of 16 cm. The formula for the volume of a cube is:
[tex]\[
\text{Volume of cubic tank} = \text{edge}^3 = 16^3 = 4096 \text{ cm}^3
\][/tex]
4. Find the volume of water required to fill [tex]\(\frac{3}{4}\)[/tex] of the cubic tank:
The cubic tank is filled to [tex]\(\frac{3}{4}\)[/tex] of its volume. Therefore, the volume of water needed is:
[tex]\[
\text{Volume of water in cubic tank} = 4096 \times \frac{3}{4} = 3072 \text{ cm}^3
\][/tex]
5. Determine the volume of water remaining in the rectangular tank:
The water poured into the cubic tank from the rectangular tank reduces the water in the rectangular tank. So, the remaining volume of water is the initial volume minus the volume transferred:
[tex]\[
\text{Remaining volume of water} = 9990 - 3072 = 6918 \text{ cm}^3
\][/tex]
6. Convert the remaining volume to liters:
Since [tex]\(1 \text{ liter} = 1000 \text{ cm}^3\)[/tex], we convert the remaining volume to liters:
[tex]\[
\text{Remaining volume in liters} = \frac{6918}{1000} = 6.918 \text{ liters}
\][/tex]
7. Round the answer:
Finally, rounding the volume to one decimal place gives approximately 6.9 liters.
So, the remaining water in the rectangular tank is approximately 6.9 liters.
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