Question

A rectangular box has faces of area 48, 60, and 80. what is its volume?

Answer 1

The volume of a rectangular box is 480 in a unit of volume

Further explanation

Given:

A rectangular box has faces of area 48, 60, and 80 in unit of area.

Question:

What is its volume?

The Process:

Let us say l = length, w = width, and h = height.

Step-1: Areas

The areas of the faces of a rectangular box are 48, 60, and 80. Therefore we can write the following equations:

• $\boxed{ \ lw = 48 \ }$
• $\boxed{ \ lh = 60 \ }$
• $\boxed{ \ wh = 80 \ }$

Step-2: Volume

The formula of volume of a rectangular box:

$\boxed{ \ V = lwh \ }$

Both sides are squared.

$\boxed{ \ V^2 = (lwh)^2 \ }$

$\boxed{ \ V^2 = l^2 \cdot w^2 \cdot h^2 \ }$

$\boxed{ \ V^2 = l \cdot l \cdot w \cdot w \cdot h \cdot h \ }$

$\boxed{ \ V^2 = l \cdot w \cdot l \cdot h \cdot w \cdot h \ }$

$\boxed{ \ V^2 = (lw)(lh)(wh) \ }$

And now, we substitute the previous three equations.

$\boxed{ \ V^2 = 48 \times 60 \times 80 \ }$

$\boxed{ \ V^2 = (3 \times 16)(4 \times 3 \times 5)(16 \times 5) \ }$

$\boxed{ \ V^2 = (3 \times 3)(4 \times 5 \times 5)(16 \times 16) \ }$

$\boxed{ \ V^2 = 3^2 \times 2^2 \times 5^2 \times 16^2 \ }$

$\boxed{ \ V^2 = (3 \cdot 2 \cdot 5 \cdot 16)^2 \ }$

Let us do square roots on both sides.

$\boxed{ \ \sqrt{V^2} = \sqrt{(3 \cdot 2 \cdot 5 \cdot 16)^2} \ }$

$\boxed{ \ V = 3 \cdot 2 \cdot 5 \cdot 16 \ }$

V = 480

Thus, the volume of a rectangular box is 480 in a unit of volume.

Based on all the steps above, remember this:

$\boxed{\boxed{ \ V^2 = (lw)(lh)(wh) \ }}$

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Notes:

A cuboid is a 3D shape. Another name is a rectangular prism. Unlike the cube, the sides of a cuboid are unequal lengths. However, the way to calculate the volume of cuboid and cube is the same, i.e., multiplying the three lengths of the sides. The other thing is to calculate the surface area by adding up all the sides.

• $\boxed{ \ Volume \ of \ cube = side \times side \times side \ }$
• $\boxed{ \ Surface \ area \ of \ cube = 6 \times area \ of \ square \ }$
• $\boxed{ \ Surface \ of \ cuboid = 2 \times [lw + lh + wh] \ }$

Learn more

1. Volume of rectangular prism  brainly.com/question/11613210
2. Find out the area of a cube  brainly.com/question/12613605#
3. Which an expression represents the height of the pyramid?  brainly.com/question/2567975

Answer 2

In order to gain volume you must simply multiply width, depth, and height. In this instances that means multiplying 60, 80, and 48. In other words you would have 230,400 (unit of measurement)^3. ^3 means cubed which is what volume is measured in. I am not sure what measurement you are using so simply fill in (unit of measurement) with whatever it is (i.e. inches=in^3, meters=m^3, etc.).