Box B length is 16 cm, width is 8 cm and height is 10 cm
The volume of box A is 40% of the volume of Box B. What is the height of Box A if the base is 32 cm?
First, we need to find the volume of Box B:
Volume of Box B = length x width x height = 16 cm x 8 cm x 10 cm = 1280 cm^3
Since the volume of Box A is 40% of the volume of Box B, the volume of Box A is:
Volume of Box A = 0.4 x 1280 cm^3 = 512 cm^3
We know that the base of Box A is 32 cm, so we can use this information to find the height of Box A. The formula for the volume of a box is:
Volume of Box = base x height
Substituting the values we know, we get:
512 cm^3 = 32 cm x height
Solving for height, we get:
height = 512 cm^3 ÷ 32 cm = 16 cm
Therefore, the height of Box A is 16 cm.
To find the height of Box A, we first need to calculate the volume of Box B:
Volume of Box B = Length x Width x Height
Volume of Box B = 16 cm x 8 cm x 10 cm
Volume of Box B = 1280 cm³
Next, we need to find 40% of the volume of Box B:
40% of Volume of Box B = (40/100) x Volume of Box B
40% of Volume of Box B = 0.4 x 1280 cm³
40% of Volume of Box B = 512 cm³
Now we know that the volume of Box A is 512 cm³. We also know that the base of Box A is 32 cm. Since the base is rectangular, we can calculate the height of Box A using the following formula:
Height of Box A = Volume of Box A / Base Area of Box A
To find the base area of Box A, we need to calculate the length and width:
Length of Box A = Base Length of Box A = 32 cm
Width of Box A = Base Width of Box A = ?
To find the width of Box A, we can use the formula:
Volume of Box A = Length x Width x Height
Plugging in the known values:
512 cm³ = 32 cm x Width of Box A x Height of Box A
Now we need to solve for the width of Box A:
Width of Box A = 512 cm³ / (32 cm x Height of Box A)
Now we can substitute the known height of Box A:
Width of Box A = 512 cm³ / (32 cm x 10 cm)
Width of Box A = 1.6 cm
Finally, we can calculate the height of Box A:
Height of Box A = Volume of Box A / (Base Length of Box A x Base Width of Box A)
Height of Box A = 512 cm³ / (32 cm x 1.6 cm)
Height of Box A = 10 cm
Therefore, the height of Box A is 10 cm.