Question

Can someone help me out with this problem How tall is a stack of cube shaped blocks whose volumes are 375 cube inches, 648 cube inches, and 1029 cube inches?

Answer 1

Answer:

The stack of blocks is 25.96 inches tall

Step-by-step explanation:

The Volume of a Cube

Given a cube-shaped figure of side length L, the volume is calculated by:

$V=L^3$

If the volume is known, then the side length can be found by solving for L:

$L=\sqrt[3]{L}$

We are given three cube-shaped blocks with known volumes. We'll find the individual side lengths and add them up to find the height that results when they stack up vertically.

Block 1, volume 375 cube inches:

$L_1=\sqrt[3]{375}=7.21\ inch$

Block 2, volume 648 cube inches:

$L_2=\sqrt[3]{648}=8.65\ inch$

Block 3, volume 1029 cube inches:

$L_3=\sqrt[3]{1029}=10.10\ inch$

Total height=7.21 inch+8.65 inch+10.10 inch=25.96 inch

The stack of blocks is 25.96 inches tall