FIND THE VOLUME OF A PYRAMID

What is a pyramid ?

A 3-dimemsional shape formed by joining all the corners of a polygon to a central point or apex is named as a pyramid.

The base of a pyramid maybe of any shape such as triangle, square, rectangle, hexagonal, etc..

What is volume of a pyramid ?

The volume V of a pyramid is one-third the area of the base B times the height h.

That is,

Volume = 1/3(area of base × height)

Find the volume of the following :

Problem 1 :

Solution :

By observing the figure, it is a cone.

Here area of base is the shape of the circle.

To find the volume,

Volume = 1/3(area of base × height)

= 1/3(area of circle × height)

= 1/3(πr× height)

we have,

radius (r) = 8 cm and height (h) = 10 cm

= 1/3(π8× 10)

= 1/3(2009.6)

Volume = 670 cm3

Problem 2 :

Solution :

By observing the figure, it is a square-based pyramid.

Here area of base is the shape of the square.

To find the volume,

Volume = 1/3(area of base × height)

= 1/3(area of square × height)

= 1/3(s× height)

we have,

side (s) = 4 cm and height (h) = 6 cm

= 1/3(4× 6)

= 1/3(96)

Volume = 32 cm3

Problem 3 :

Solution :

By observing the figure, it is a cone.

Here area of base is the shape of the circle.

To find the volume,

Volume = 1/3(area of base × height)

= 1/3(area of circle × height)

= 1/3(πr× height)

we have,

radius (r) = 5 cm and height (h) = 11 cm

= 1/3(π5× 11)

= 1/3(863.5)

Volume = 288 cm3

Problem 4 :

Solution :

By observing the figure, it is a square-based pyramid.

Here area of base is the shape of the square.

To find the volume,

Volume = 1/3(area of base × height)

= 1/3(area of square × height)

= 1/3(s× height)

we have,

side (s) = 5 cm and height (h) = 7 cm

= 1/3(5× 7)

= 1/3(175)

Volume = 58.3 cm3

Problem 5 :

Solution :

By observing the figure, it is a hexagonal pyramid.

Here area of base is the shape of the hexagonal.

To find the volume,

Volume = 1/3(area of base × height)

we have,

area = 32 cm2 and height (h) = 8 cm

= 1/3(32 × 8)

= 1/3(256)

Volume = 85.3 cm3

Problem 6 :

Solution :

By observing the figure, it is a rectangle-based pyramid.

Here area of base is the shape of the rectangle.

To find the volume,

Volume = 1/3(area of base × height)

= 1/3(area of rectangle × height)

= 1/3(length × width × height)

we have,

length (l) = 4 cm, width (w) = 2 cm and height (h) = 9 cm

= 1/3(4 × 2 × 9)

= 1/3(72)

Volume = 24 cm3

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