Answer:
The height of the pyramid is 2cm
Step-by-step explanation:
From the complete question, we have:
Marble Dimension:
[tex]Length = Width = 6cm[/tex]
[tex]Height = 8cm[/tex]
Pyramid
[tex]Length = Width = 6cm[/tex]
Volume = 1/4th of the volume of the marble
Required
The height of the pyramid
First, calculate the volume of the Marble
[tex]Volume = Length * Width *Height[/tex]
So:
[tex]V_1 = 6cm * 6cm * 8cm[/tex]
[tex]V_1 = 288cm^3[/tex]
Calculate the volume of the Pyramid
[tex]Volume = Length * Width *Height[/tex]
[tex]V_2 = 6cm * 6cm * h\ cm[/tex]
[tex]V_2 = 36cm^2 h[/tex]
From the question, we understand that:
[tex]V_2 = \frac{V_1}{4}[/tex]
So, we have:
[tex]36cm^2h = \frac{288cm^3}{4}[/tex]
[tex]36h = \frac{288cm}{4}[/tex]
[tex]36h = 72cm[/tex]
Solve for h
[tex]h = \frac{72cm}{36}[/tex]
[tex]h =2cm[/tex]
