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
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