If a cube and a square pyramid have the same square base and the same height, the volume of the cube will be ___ times as large as the volume of the pyramid. *

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

Where

= Volume

= Base Edge

= 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:

V =

V=

Volume for Pyramid = 21.333

C) Volume for Cube

Recall that the formula for calculating the volume of a cube is given as:

Where is the value of the side.

Recall that our elected value is 4

Therefore,

= 4 x 4 x 4

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!

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.