Find the total surface area if q solid cube of volume 98 cm cube.
An open water tank with length 20 cm and width 15 cm holds 4.8 liters of water. Calculate the height of the water level in tank and the total sitface area of the cuboid in contact with water.
4.8 litres = 4.8*1000 cm³=4800 cm³
Volume = width*length*height,
therefore
height=volume/(width*length)
=4800 cm³/(15 cm * 20 cm)
=16 cm
Total side surface area
= sum of area of 4 vertical faces
= 2(height*length+height*width)
= 2(16cm*15cm+16cm*20cm)
= 2(240+320)
= 1120 cm²
For the cube, it is not clear to me if the volume is 98 cm³ or (98cm)³.
In any case, if
V=volume,
side, s = ∛V
total surface area = 6*s²
To find the total surface area of a solid cube with a volume of 98 cm³, we need to calculate the length of one side of the cube first.
The volume of a cube is given by the formula:
Volume = length³
98 cm³ = length³
To find the length, we can take the cube root of both sides:
length = ∛(98 cm³)
Using a calculator, the cube root of 98 is approximately 4.62 cm.
Now, to calculate the total surface area of the cube, we use the formula:
Surface Area = 6 * (length²)
Substituting the length we found:
Surface Area = 6 * (4.62 cm)²
Using a calculator, the surface area of the cube is approximately 268.59 cm².
Now, moving on to the second question.
To calculate the height of the water level in an open tank, we need to find the volume of water and then divide it by the base area of the tank.
Given dimensions:
Length = 20 cm
Width = 15 cm
Volume of water = 4.8 liters
First, we convert the volume from liters to cubic centimeters (1 liter = 1000 cm³):
Volume of water = 4.8 liters * 1000 cm³/liter = 4800 cm³
Now, we can find the height of the water level:
Height = Volume of water / Base area
The base area of a rectangle is given by multiplying the length and width:
Base area = Length * Width = 20 cm * 15 cm = 300 cm²
Height = 4800 cm³ / 300 cm²
Using division, the height of the water level is approximately 16 cm.
To find the total surface area of the cuboid in contact with water, we need to calculate the surface area of the top, bottom, and sides of the tank.
The total surface area can be calculated using the formula:
Surface Area = 2 * (Length * Width) + 2 * (Length * Height) + 2 * (Width * Height)
Substituting the given values:
Surface Area = 2 * (20 cm * 15 cm) + 2 * (20 cm * 16 cm) + 2 * (15 cm * 16 cm)
Using multiplication and addition, the total surface area of the cuboid in contact with the water is approximately 1500 cm².
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.