Question

The dimensions of two square pyramids formed of sand are shown. How much more sand is in the pyramid with the greater volume?

Answer 1

The pyramid with the greater volume has 5in^3 more sand

Explanation:

Given

Pyramid A

`B = 25in^2` -- Base Area

`h = 9in` --- height

Pyramid B

`B = 30in^2`

`h = 7in`

See attachment for pyramids

The volume of a square pyramid is:

`V = (1)/(3)Bh`

First, calculate the volume of pyramid A

`V_A = (1)/(3) * 25in^2 * 9in`

`V_A = 25in^2 * 3in`

`V_A = 75in^3`

Next, the volume of pyramid B

`V_B = (1)/(3) * 30in^2 * 7in`

`V_B = 10in^2 * 7in`

`V_B = 70in^3`

To calculate how much more sand the greater pyramid has, we simply calculate the absolute difference (d) between their volumes

`d = |V_B - V_A|`

`d = |70in^3 - 75in^3|`

`d = |- 5in^3|`

`d = 5in^3`