Question

a) which expression represents the volume of amelias flowerpot? 5×5×5
b) what is the volume of amelias flowerpot?
c) v = 125 in³
d) let s equal the side length of a cube. which expression can you use to find the volume of a cube?
s + s + s + s + s + s
s + s + s
2·s
s·s·s

Explanation:

Sub - question 1: Which expression represents the volume of Amelia's flowerpot?

Step 1: Identify the shape

Amelia's flowerpot is a cube (since all sides are 5 in as seen from the diagram). The formula for the volume of a cube with side length \( s \) is \( V=s\times s\times s \) (or \( V = s^{3}\)). Here, \( s = 5 \) inches, so the expression for the volume is \( 5\times5\times5 \).

Step 1: Use the volume formula for a cube

The formula for the volume of a cube is \( V=s\times s\times s \), where \( s = 5 \) inches.

Step 2: Calculate the volume

Substitute \( s = 5 \) into the formula: \( V=5\times5\times5=125 \) cubic inches.

• The formula for the volume of a cube with side length \( s \) is based on the fact that a cube has length, width, and height all equal to \( s \). The volume of a rectangular prism (and a cube is a special case of a rectangular prism) is \( V = l\times w\times h \). For a cube, \( l=w = h=s \), so \( V=s\times s\times s \).
• The expression \( s + s+ s \) is the formula for the perimeter of one face (or the sum of the side lengths of one dimension), not volume.
• The expression \( 2\cdot s \) is related to the perimeter of a line segment or a very basic linear measure, not volume.
• The expression \( s + s+ s + s + s + s \) is the total length of all 12 edges (since a cube has 12 edges, 4 of each dimension) summed up, not volume.

Answer:

\( 5\times5\times5 \)

Sub - question 2: What is the volume of Amelia's flowerpot?