Formula For Volume Of Pyramid

A pyramid is a three-dimensional polyhedron with a polygonal base and 3 or more triangle-shaped faces that meet in a higher place the base of operations. The faces are the triangle sides, while the apex is the point above the base. The base is continued to the tiptop to grade a pyramid. When the pyramid's base is in the shape of a foursquare, the pyramid is called a square pyramid. Ane foursquare base of operations and three triangular faces make up a square pyramid. It contains 8 edges, 5 vertices, and 4 faces, in other words.

Volume of a Square Pyramid Formula

The space independent betwixt the five faces of a square pyramid is referred to every bit its book. Knowing the base of operations expanse and height of a square pyramid is all that is required to summate its volume. The volume of a square pyramid is equal to one-third of the product of the base of operations'south area and the pyramid's height.

Formula

V = (i/3) × a² × h

where,

a is the length of the square base of operations,

h is the height (or altitude).

Sample Problems

Problem 1. Find the volume of a square pyramid if the length of its base is 6 cm and its height is iv cm.

Solution:

We accept, a = 6 and h = iv.

Using the formula we have,

5 = (1/3) × a² × h

= (one/3) × 6² × four

= (1/3) × 36 × 4

= 12 × iv

= 48 cm³

Trouble 2. Observe the book of a foursquare pyramid if the length of its base is 12 cm and the height is 15 cm.

Solution:

We have, a = 12 and h = xv.

Using the formula we have,

V = (1/3) × a² × h

= (1/3) × 12² × 15

= (1/3) × 144 × xv

= 144 × 5

= 720 cm³

Problem 3. Find the length of the base of a square pyramid if its book is 1125 cm³ and height is fifteen cm.

Solution:

Nosotros have, Five = 1125 and h = 15.

Using the formula we have,

V = (1/iii) × a² × h

=> 1125 = (ane/3) × a² × 15

=> 1125 = (1/iii) × a² × 15

=> 1125 = 5aⁱⁱ

=> aⁱⁱ = 225

=> a = 15 cm

Trouble 4. Discover the height of a foursquare pyramid if its volume is 1372 cm³ and base of operations length is fourteen cm.

Solution:

We have, V = 1372 and a = fourteen.

Using the formula we have,

V = (1/3) × aⁱⁱ × h

=> 1372 = (1/3) × 14 × 14 × h

=> 1125 = (1/3) × 196 × h

=> 196 h = 4116

=> h = 21 cm

Problem 5. Find the area of the base of a square pyramid if its book is 98 cmⁱⁱⁱ and height is half dozen cm.

Solution:

We have, V = 98 and h = half dozen.

Using the formula nosotros have,

V = (one/3) × aⁱⁱ × h

=> 98 = (1/iii) × aⁱⁱ × 6

=> 98 = 2aⁱⁱ

=> a² = 49 sq. cm