Question

a cylinder with a volume of 640 cubic centimeters is dilated by a scale factor of 2. what is the volume, in cubic centimeters, of the new cylinder?

Explanation:

Step1: Recall volume dilation rule

For a 3D object, when dilated by a scale factor \( k \), the volume scales by \( k^3 \). Here, \( k = 2 \), so volume scale factor is \( 2^3=8 \).

Step2: Calculate new volume

Original volume \( V = 640 \, \text{cm}^3 \). New volume \( V_{\text{new}}=640\times8 \).
\( 640\times8 = 5120 \).

Answer:

5120