Respuesta :
Answer:
3 times
Explanation:
The volume of a Cube is given by length * length * length
Mathematically,
V (cube) = l³
where:
V = volume, l = length
The volume of a Square Pyramid is given by the product of ⅓ by length² by height
Mathematically,
V (square pyramid) = ⅓ * l² * h
where:
V = volume, length = l, height = h
Assuming l = h; V (square pyramid) = ⅓ * l³
The ratio of volume of Cube to volume of Square Pyramid is given by:
l³ ÷ (⅓ * l³) = 1 ÷ ⅓ = 3
It implies that, if the square base & height of both the cube & pyramid are the same, the volume of the Cube is thrice (3x) as large as the Square Pyramid.
Hence, if a cube and a square pyramid have the same square base and the same height, the volume of the cube will be 3 times as large as the volume of the pyramid.
Answer:
The volume of the cube will be approximately 3 times as large as the volume of the pyramid.
Step-by-step explanation:
To prove the above, we'd need to perform some simple calculations.
Step I - Calculate the Volumes for both Pyramid and Cube
A) Volume for Pyramid
The formula for calculating the volume of a pyramid with a square base is
[tex]V = a^{2}\frac{h}{3}[/tex]
Where
[tex]v[/tex] = Volume
[tex]a[/tex]= Base Edge
[tex]h[/tex] = Height
B)
Recall that the square pyramid has the same square base and the same height.
So assuming a fictitious value of 4 for both square base and height, we have:
[tex]V = 4^{2} (\frac{4}{3})[/tex]
V = [tex]\frac{16 X 4 }{3}[/tex]
V= [tex]\frac{64}{3}[/tex]
Volume for Pyramid = 21.333
C) Volume for Cube
Recall that the formula for calculating the volume of a cube is given as:
[tex]V = a^{3}[/tex]
Where [tex]a[/tex] is the value of the side.
Recall that our elected value is 4
Therefore,
[tex]V =[/tex] [tex]4^{3}[/tex]
[tex]V[/tex] = 4 x 4 x 4
[tex]V =[/tex] 64
Step II - Compare Volume of the Sqare Pyramid with Volume of the Cube
Volume of the Square Pyramid = 21.333
Volume of the Cube = 64
Obviously the volume of the Cube is larger. To get the extent by the cube is more voluminous, we divide volume of the Cube by that of the Square Pyramid.
That is:
64/21.333
= 3.00004687573
or 3 when approximated to the nearest digit.
So, the volume of the cube is approximately 3 times as large as the volume of the pyramid.
Cheers!
