A square pyramid has a height of 6 units and a volume of 70 units3. If a square prism has the same base area and volume as the square pyramid, what is its height? 2 units 4 units 6 units 8 units

2 units

Step-by-step explanation:

⅓base area × 6 = 70

Base area = 35

70 = 35h

h = 2

2 units

Step-by-step explanation:

A square pyramid has a height of 6 units and a volume of 70 unit³.

The volume of a square base pyramid is defined as follows :

volume = A(h/3)

where A = area of the base shape(square)

h = height

volume = 70 unit³

h = 6 unit

70 = A (6/3)

70 = 2A

divide both sides by 2

A = 70/2

A = 35

The side of the base shape square can be calculated from the area

L² = 35

L = √35

A square base prism has the same base area and volume of the square pyramid . Therefore, the height can be computed as follows:

volume of a square base prism = a2 h

where

a = side of the base

h = height of the prism

volume of the prism = a²h

70 =  (√35)²h

70 = 35h

divide both sides by 35

h = 70/35

h = 2 units

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