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

Answer:

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

Step-by-step 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:

$V = \frac{1}{3}Bh$

First, calculate the volume of pyramid A

$V_A = \frac{1}{3} * 25in^2 * 9in$

$V_A = 25in^2 * 3in$

$V_A = 75in^3$

Next, the volume of pyramid B

$V_B = \frac{1}{3} * 30in^2 * 7in$

$V_B = 10in^2 * 7in$

$V_B = 70in^3$

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

$d = |V_B - V_A|$

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

$d = |- 5in^3|$

$d = 5in^3$