Let's solve the problem step by step:
### Part (i): Volume of water in the tank
1. Determine the volume in cubic centimeters:
The volume of a rectangular prism (or tank) is calculated by multiplying its length, width, and height.
[tex]\[
\text{Volume (cm}^3\text{)} = \text{length} \times \text{width} \times \text{height}
\][/tex]
Given:
[tex]\[
\text{length} = 80 \text{ cm}, \quad \text{width} = 40 \text{ cm}, \quad \text{height} = 35 \text{ cm}
\][/tex]
Thus,
[tex]\[
\text{Volume (cm}^3\text{)} = 80 \times 40 \times 35 = 112000 \text{ cm}^3
\][/tex]
2. Convert the volume from cubic centimeters to liters:
Since 1 liter is equivalent to 1000 cubic centimeters,
[tex]\[
\text{Volume (liters)} = \frac{\text{Volume (cm}^3\text{)}}{1000}
\][/tex]
Substituting the value we have,
[tex]\[
\text{Volume (liters)} = \frac{112000}{1000} = 112.0 \text{ liters}
\][/tex]
So, the volume of water in the tank is [tex]\( 112.0 \text{ liters} \)[/tex].
### Part (ii): Surface area of the tank in contact with the water
1. Determine the total surface area in contact with the water in square centimeters:
The surface area in contact with the water includes:
- The bottom of the tank (one face),
- The four vertical sides in contact with the water.
Bottom area:
[tex]\[
\text{Area}_{\text{bottom}} = \text{length} \times \text{width} = 80 \times 40 = 3200 \text{ cm}^2
\][/tex]
The four vertical sides (excluding the top surface) consist of:
- Two sides of area [tex]\( \text{length} \times \text{height} \)[/tex]:
[tex]\[
\text{Area}_{\text{side-1}} = 2 \times (80 \times 35) = 5600 \text{ cm}^2
\][/tex]
- Two sides of area [tex]\( \text{width} \times \text{height} \)[/tex]:
[tex]\[
\text{Area}_{\text{side-2}} = 2 \times (40 \times 35) = 2800 \text{ cm}^2
\][/tex]
Adding these areas together:
[tex]\[
\text{Total surface area}_{\text{cm}^2} = \text{Area}_{\text{bottom}} + \text{Area}_{\text{side-1}} + \text{Area}_{\text{side-2}}
\][/tex]
[tex]\[
\text{Total surface area}_{\text{cm}^2} = 3200 + 5600 + 2800 = 11600 \text{ cm}^2
\][/tex]
2. Convert the surface area from square centimeters to square meters:
Since 1 square meter is equivalent to 10,000 square centimeters,
[tex]\[
\text{Surface area (m}^2\text{)} = \frac{\text{Surface area (cm}^2\text{)}}{10000}
\][/tex]
Substituting the value we have,
[tex]\[
\text{Surface area (m}^2\text{)} = \frac{12000}{10000} = 1.2 \text{ m}^2
\][/tex]
So, the surface area of the tank that is in contact with the water is [tex]\( 1.2 \text{ m}^2 \)[/tex].
### Summary
(i) The volume of water in the tank is 112.0 liters.
(ii) The surface area of the tank that is in contact with the water is 1.2 m².
