To find the total surface area of a solid cube, you need to know the volume of the cube. The formula for the volume of a cube is:
Volume = side^3
In this case, the volume is given as 98 cm^3. By rearranging the formula, we can solve for the side length of the cube:
side = cube root of volume
So in this case:
side = cube root of 98 cm^3
Using a calculator, we find that the cube root of 98 is approximately 4.62 cm.
To find the total surface area of the cube, you can use the following formula:
Surface Area = 6 * side^2
Substituting the value of the side length we obtained earlier, we have:
Surface Area = 6 * (4.62 cm)^2
Calculating this gives us a total surface area of approximately 128.35 cm^2.
Now, let's move on to the second part of your question regarding the open water tank.
To find the height of the water level in the tank, we need to convert the volume of water from liters to cubic centimeters (cm^3) because the dimensions of the tank are given in cm.
1 liter = 1000 cubic centimeters
So 4.8 liters of water is equal to 4800 cm^3.
The volume of the tank is given by its length, width, and height:
Volume = length * width * height
In this case, the volume is known as 4800 cm^3, while the length and width are given as 20 cm and 15 cm, respectively. By rearranging the formula, we can solve for the height of the water level:
height = volume / (length * width)
Plugging in the values, we have:
height = 4800 cm^3 / (20 cm * 15 cm)
This gives us a height of approximately 16 cm for the water level in the tank.
Finally, to calculate the total surface area of the cuboid in contact with the water, you need to find the surface area of the top and the four sides (assuming the bottom is not in contact with water). The formula for the surface area of a cuboid is:
Surface Area = 2 * (length * width + length * height + width * height)
Plugging in the values, we have:
Surface Area = 2 * (20 cm * 15 cm + 20 cm * 16 cm + 15 cm * 16 cm)
Calculating this gives us a total surface area of approximately 1460 cm^2.