these solids are similar. find the volume of the larger solid. \nlarger cone: h = 15 m, v = ? m³\nsmaller…

Explanation:

Step1: Find scale factor

The scale factor of the larger solid to the smaller solid is the ratio of their heights: $\text{Scale factor} = \frac{15}{6} = \frac{5}{2}$

Step2: Find volume scale factor

For similar solids, the ratio of volumes is the cube of the linear scale factor: $\text{Volume scale factor} = \left(\frac{5}{2}\right)^3 = \frac{125}{8}$

Step3: Calculate larger volume

Multiply the smaller volume by the volume scale factor: $V_{\text{larger}} = 40 \times \frac{125}{8}$

Answer:

$625 , \text{m}^3$