Answer:
The pyramid with the greater volume has 5in^3 more sand
Step-by-step explanation:
Given
Pyramid A
[tex]B = 25in^2[/tex] -- Base Area
[tex]h = 9in[/tex] --- height
Pyramid B
[tex]B = 30in^2[/tex]
[tex]h = 7in[/tex]
See attachment for pyramids
The volume of a square pyramid is:
[tex]V = \frac{1}{3}Bh[/tex]
First, calculate the volume of pyramid A
[tex]V_A = \frac{1}{3} * 25in^2 * 9in[/tex]
[tex]V_A = 25in^2 * 3in[/tex]
[tex]V_A = 75in^3[/tex]
Next, the volume of pyramid B
[tex]V_B = \frac{1}{3} * 30in^2 * 7in[/tex]
[tex]V_B = 10in^2 * 7in[/tex]
[tex]V_B = 70in^3[/tex]
To calculate how much more sand the greater pyramid has, we simply calculate the absolute difference (d) between their volumes
[tex]d = |V_B - V_A|[/tex]
[tex]d = |70in^3 - 75in^3|[/tex]
[tex]d = |- 5in^3|[/tex]
[tex]d = 5in^3[/tex]
