What is the height of a cubiod whose cross-sectional area is 48cm square and volume is 216m cube
We need to convert the volume to cubic centimeters since the cross-sectional area is given in square centimeters.
1 m = 100 cm
Volume = 216 m^3 = 216000000 cm^3
Let the height be h, length be l, and width be w of the cuboid.
Cross-sectional area = lw = 48 cm^2
Since the cross-sectional area is equal to length times width, we can express the length in terms of the width:
l = 48/w
Volume = lwh = (48/w)wh = 48h cm^3
We can now substitute the volume value:
48h = 216000000
h = 4500000 cm
Therefore, the height of the cuboid is 4500000 cm or 45 km.
To find the height of the cuboid, we need to know the formula for the volume of a cuboid.
The formula for the volume of a cuboid is given by:
Volume = Length x Width x Height
Given that the volume of the cuboid is 216 m^3, we can rearrange the formula to solve for the height:
Height = Volume / (Length x Width)
However, we need to first convert the cross-sectional area from cm^2 to m^2, since the volume is given in cubic meters.
Cross-sectional area = 48 cm^2
To convert it to m^2, divide it by 10,000 (since 1 m^2 = 10,000 cm^2):
Cross-sectional area = 48 cm^2 / 10,000 = 0.0048 m^2
Now, we can find the length and width. Since the cross-sectional area of a rectangle is equal to the length multiplied by the width, we can say:
Length x Width = Cross-sectional area
Substituting the values:
Length x Width = 0.0048 m^2
Now we have two equations:
Volume = Length x Width x Height
0.0048 = Length x Width
Given that the volume is 216 m^3, we can plug in the values and solve for height:
216 = Length x Width x Height
0.0048 = Length x Width
Let's solve for Length and Width from the second equation:
Length = 0.0048 / Width
Now substitute Length into the first equation:
216 = (0.0048 / Width) x Width x Height
Simplifying the equation:
216 = 0.0048 x Height
To isolate Height, divide both sides of the equation by 0.0048:
Height = 216 / 0.0048
Solving for Height:
Height = 45,000 m
So, the height of the cuboid is 45,000 meters.