How to find the height of a box?

Mathematics deals with all the universal calculations. Accordingly, the matter of dealing with mathematics is divided into different branches like algebra, geometry, arithmetic, etc. Among this mensuration is a branch that deals with the calculation of parameters like perimeter, area, volume, etc. of various shapes whether it be two-dimensional or three-dimensional.

In two-dimensional shapes, objects comprise of length and width or any two dimensions that can be represented on a plane surface. While, three-dimensional shapes, objects are placed in the real world and have three dimensions that are length, width, and height.

Some Basic formulas for 2D and 3D shapes

2D Shapes	Formulas
Rectangle	Area = length × breadth Perimeter = 2(length+breadth)
Square	Area = (side)2 Perimeter = 4(side)
Triangle	Area = 1/2 breadth × height
Circle	Diameter = 2 × radius Area = π × (radius)2

3D Shapes	Formula
Cube	Volume = (side)3 Lateral surface area = 4 × (side)2 Total surface area = 6 × (side)2
Cuboid	Volume = length × breadth × height Lateral surface area = 2 × height(l+b) Total surface area = 2(lb+lh+hb)
Sphere	Volume = 4/3πr3 Surface area = 4πr2
Cone	Volume = 1/3πr2h Total surface area = πr (l+radius)

What is the height of an object?

Height is one of the three integral dimensions for determining the volume of an object. Mathematically, the height of any geometrical shape whether it be a cube, cuboid, or pyramid can be calculated with certain volume formula.

How to find the height of a box?

If the box given is a rectangular box or a cuboid we can simply find out its height by dividing the volume of the box by-product of length and breadth. As the volume formula for cuboids is length × breadth × height.

Mathematically,

Volume of cuboid = Length × breadth × height

=>V = l × b × h

For determining height

=>h = V/b × h

Similarly, if the given box is a square box or a cube then we can calculate its height by finding the cube root of its volume. As a cube has its all sides equal and its volume is determined by a cube of side.

Mathematically,

The volume of cube = (side)³

=>height = ³√(volume)

Sample Problems

Problem 1. Find the height of a cuboid with length 20 cm, breadth 10 cm, and volume 6000cm³.

Solution:

Given,

length(l) = 20cm

breadth(b) =10cm

Volume(V) = 6000cm³

height(h) = ?

Now,

V = l × b × h

=>h = V/b × h

=>h= 6000/ 10 × 20

=>h = 6000/200

=>h = 30cm

Problem 2. Calculate the height of a cube box if its volume is 27cm³.

Solution:

Given,

volume of cube(V) = 27 cm³

As we know that all sides of a cube are equal

Volume of cube (V) = (side)³

=> 27 = (side)³

=>side=

=>side=

=>side = 3cm

or, height of cube box = 3cm

Problem 3. A cuboid of volume 1200cm³ has a length of 10cm and breadth of 8cm. Find its height.

Solution:

Given,

length (l)=10cm

breadth(b)=8cm

Volume(V)=1200cm³

Height(h)=?

Now,

V = l × b × h

=>h = V/ l × b

=> h = 1200/10 × 8

=>h = 1200/80

=>h = 15cm

Problem 4. A box having height 3 inches, width 2 inches, and length 6 inches is placed on the floor. Calculate the volume of the box.

Solution:

Given, 

height(h)= 3inches

width(b)= 2 inches

length(l)= 6inches

Volume(V)=?

Now,

Volume(V)= l × b × h

=>V = 3 × 2 × 6

=>V = 36 inches³