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^{2 }× height)
we have,
radius (r) = 8 cm and height (h) = 10 cm
= 1/3(π8^{2 }× 10)
= 1/3(2009.6)
Volume = 670 cm^{3}
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^{2 }× height)
we have,
side (s) = 4 cm and height (h) = 6 cm
= 1/3(4^{2 }× 6)
= 1/3(96)
Volume = 32 cm^{3}
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^{2 }× height)
we have,
radius (r) = 5 cm and height (h) = 11 cm
= 1/3(π5^{2 }× 11)
= 1/3(863.5)
Volume = 288 cm^{3}
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^{2 }× height)
we have,
side (s) = 5 cm and height (h) = 7 cm
= 1/3(5^{2 }× 7)
= 1/3(175)
Volume = 58.3 cm^{3}
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 cm^{2} and height (h) = 8 cm
= 1/3(32^{ }× 8)
= 1/3(256)
Volume = 85.3 cm^{3}
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 cm^{3}
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