A prism with volume \( 360 \mathrm{~cm}^{3} \) is dilated with a factor of \( \frac{1}{3} \). What is the volume of the image? Express your answer to the nearest two decimal places. \( 13.3 \mathrm{~cm}^{3} \) \( 27.03 \mathrm{~cm}^{3} \). \( 13.33 \mathrm{~cm}^{3} \) \( 27.3 \mathrm{~cm}^{3} \) Hide hint forQuestion 3 The volume of the dilated image will be \( \left(\frac{1}{3}\right)^{3} \), or \( \frac{1}{27} \), the volume of the orig image.

When a prism undergoes dilation, the volume scales with the cube of the linear dilation factor. In this case, the factor is \( \frac{1}{3} \), so we calculate \( \left(\frac{1}{3}\right)^3 = \frac{1}{27} \). To find the volume of the dilated prism, multiply the original volume, \( 360 \mathrm{~cm}^{3} \), by \( \frac{1}{27} \), resulting in \( \frac{360}{27} \approx 13.33 \mathrm{~cm}^{3} \). Dilation can be an exciting concept, especially when you visualize it! Imagine an oversized sponge being shrunk down to the size of a small sponge. While all dimensions shrink, their proportional relationship is maintained, and just as we calculated, the volume decreases drastically! Each side's length being reduced to a fraction means that the overall size — the volume — experiences a more significant change. Hence, keep your eye on those factors when dilating!