Which Expression Represents the Volume of the Pyramid.

The

**book of a pyramid**

depends upon the type of pyramid’southward base, whether it is a triangle, square or rectangle. A pyramid is a polyhedron figure which has only ane base. The base of operations of the pyramid is a poly sided figure. Hence, the formula to find not only book but likewise the expanse of a pyramid will be based on the structure of its base of operations and acme of the pyramid.

At present allow us find out the formula for the triangular pyramid, square pyramid and rectangular pyramid in this article.

- Derivation
- Formula
- Triangular Pyramid
- Square Pyramid
- Rectangular Pyramid
- Hexagonal Pyramid

- Examples

Contents

## Derivation of Volume of a Pyramid

To observe the volume of a pyramid, we need to know the full chapters of the given pyramid. The formula for the pyramid’s volume is given past one-third of the product of the area of the base to its peak. Such as:

Volume = 1/3 x Area of the Base ten Superlative

Where V = Volume, A = Surface area and H = height

Its book is measured in the following units:

- in
^{3} - ft
^{iii} - cm
^{iii} - m
^{iii}

etc

Note: Ever make sure to proceed all the measurement units same while calculating the volume.

Now let us observe out the formula for the volume of dissimilar types of pyramids.

## Volume of Pyramid Formula

Pyramids are of unlike types, such as:

- Triangular Pyramid
- Square Pyramid
- Rectangular Pyramid
- Hexagonal Pyramid

For all these types of pyramids, the formula for book is different. Allow u.s.a. learn here all the book formulas.

### Volume of Triangular Pyramid

A triangular pyramid has a base in triangle shape. As we know, the area of a triangle;

A = ane/2 b x h

where b is the base of the triangle and h is the altitude.

Therefore, the book of a triangular pyramid;

5 = i/3 x Area of triangular base of operations 10 Meridian of pyramid

V = 1/3 10 (i/2 bh) H

**5 = 1/vi bhH**

### Volume of Square Pyramid

A square-based pyramid has a base of operations in square shape. As we know, the surface area of a foursquare is given by;

A = a^{2}

Where a is the length of the side of the square.

Hence, the volume of a square-sided pyramid is;

V = 1/3 ten Area of square base of operations x Height

5 = i/3 ten a^{2}

10 H

**V = ane/iii a ^{2} H**

### Volume of the Rectangular Pyramid

A rectangular pyramid has the base of operations in a rectangular shape. Since, we know that the area of rectangle is equal to the product of its length and width, such as;

A = Length ten Width

A = lw

Hence, the volume of a rectangular pyramid is given by;

V = one/3 x A x H

**Five = one/iii lwH**

### Book of Hexagonal Pyramid

The volume of a hexagonal pyramid, whose base is a regular hexagon shape is given by:

Book = 1/3 ten area of base of operations ten meridian

V= ane/three x 3√3/ii a^{2} x H

Five = √iii/2 a^{2} H

Where a is the side length of the hexagon base and H is the height of the pyramid.

**Also, read:**

- Pyramid
- Pyramid Formula
- Triangular Pyramid Formula
- Volume of A Foursquare Pyramid

### Examples

**Question i**:

What is the volume of a pyramid whose base of operations is square? The sides of the base of operations are x cm each and the height of the pyramid is 18 cm.

**Solution:**

To find the volume of a pyramid, Nosotros will use the formula – V = ⅓ A H

As the base of the pyramid is a square, the surface area of the base is a^{ii
}

= 10 x ten = 100 cm^{2}

= ⅓ 10 100 cm

^{2}

x eighteen cm

= 100 10 6

= 600 cm^{3}

**Question 2: What is the volume of a pyramid whose base is square? The sides of the base are 12 cm each and the height is 21 cm**.

**Solution:**

To find the volume of a pyramid, We volition use the formula – V = ⅓ A H

As the base of operations of the pyramid is a square, the expanse of the base is a^{ii
}

= 12 x 12 = 144 cm^{2}

= ⅓ x 144 cm

^{2}

x 21 cm

= 144 x 7

= 1008 cm^{three}

**Question 3: If the base of the pyramid is rectangular having length is 7 cm and the width is 5 cm and the peak of the pyramid is ten cm, then find its book.**

Solution: Given, length of rectangular base of pyramid = 7 cm

width = v cm

and height of the pyramid = ten cm

We know, the volume of rectangular pyramid,

V = 1/iii l westward H

Substituting the values we get;

V = 1/three ten 7 x 5 10 10

V = 350/iii = 116.66 cubic.cm.

**Question 4: For the triangular pyramid, the area of the base is 135 cubic cm. Find its volume if the tiptop of pyramid is seven cm.**

Solution: Given the area of the base of pyramid = 135 cu.cm

Volume of Pyramid = 1/iii x A ten H

V = 1/3 x 135 x 7

5 = 45 x 7

Five = 315 Cu. Cm.

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## Which Expression Represents the Volume of the Pyramid

Source: https://byjus.com/maths/volume-of-a-pyramid/