Question

Two square based pyramids are joined, total volume is 2700mm, perpendicular height 16mm on top pyramid and 20mm on the other, joint base has length and width of x, find x. Please help me..

Answer 1

15 mm

Explanation:

Since both pyramids are joined together, this means that the base of the pyramid which is a square have the same dimensions.

Let the length and width of the base be x, hence the dimension of the base is x mm by x mm.

For the first pyramid, the volume is:

V₁ = a²h₁/3; where a is the length of the square base, h₁ is the height.

Since the pyramid has a height of 16 mm, hence:

V₁ = 16x²/3

the second pyramid, the volume is:

V₂ = a²h₂/3; where a is the length of the square base, h₂ is the height.

Since the pyramid has a height of 20 mm, hence:

V₂ = 20x²/3

Since the total volume (V) of the pyramid is 2700 mm³, hence:

V = V₁ + V₂

V = 16x²/3 + 20x²/3

2700 = 16x²/3 + 20x²/3

2700 = 36x²/3

36x² = 8100

x² = 225

x = 15 mm