Question

A rectangular square pyramid is 3m. Height and perimeter of the base is 16m. Find the volume of the pyramid

Answer 1

Volume of Pyramid

Volume of Pyramid : (Pyramid ) : There are different types of pyramid, depending on their bases. If the base is triangle then it is called triangular pyramid . If base is rectangle then it is called as rectangular pyramid and so on.



Volume of these solids are depending on the area of their bases.
Volume of triangular PyramidV = 1/3 x Area of triangular base x height(H)
V = 1/3( base x height) / 2 x HVolume of Hexagonal PyramidV = 1/3 x Area of hexagon x H 
V = 6 x (√3 / 4 ) (side)2 x H 
V = 1/3(AP/ 2) x H ( A = apothem ; P = perimeter)Volume of Pentagonal PyramidVolume = 1/3 x area of base x height(H)
V = 1/3 (AP/ 2) x H ( A = apothem ; P = perimeter)
Some solved examples 

1) If the length of each side of the base of a triangular pyramid is 6 cm and its height is 10 cm, find its volume. ( √3 = 1.73)
Solution : 
Area of base = √3 / 4 x (side)2 
⇒ Area = √3 / 4 x (6)2
⇒ Area = √3 /4 x 36 
∴ Area = 9 √3 cm2 
Pyramid volume = 1/3 x area of base x height 
⇒ Pyramid volume = 1/3 x 9 √3 x 10 
⇒ Volume = 30 √3 
⇒ Volume = 30 x 1.73
⇒ Volume = 51.9 cm3
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2) If the length of each side of a square pyramid is 4 cm and its height is 12 cm.
Solution : 
Area of base = side x side 
⇒ Area = 4 x 4 
⇒ Area = 16 cm2
Pyramid volume = 1/3 x area of base x height 
⇒ Volume = 1/3 x 16 x 12
⇒ Volume = 64 cm3
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3) Find the volume of a regular hexagonal pyramid with an apothem length of 6 cm,
side 3 cm and height of the pyramid is 21 cm.
Solution : 
apothem = A = 6 cm and side = 3 cm height = H =21 cm
Perimeter = 3 x 6 = 18 cm 
Area of Base (hexagon) = AP /2 
⇒ Area = (6 x 18 )/2 
⇒ Area = 54 cm2 
volume of pyramid=1/3 x( Area of base) x H
∴ V = 1/3 x 54 x 21 
∴ Volume = 378 cm3