these solids are similar. find the volume of the larger solid. h = 4 cm v = ? cm³ h = 3 cm v = 27 cm³

Explanation:

Step1: Find scale factor

Scale factor $k = \frac{\text{Height of larger solid}}{\text{Height of smaller solid}} = \frac{4}{3}$

Step2: Find volume scale factor

Volume scale factor = $k^3 = \left(\frac{4}{3}\right)^3 = \frac{64}{27}$

Step3: Calculate larger volume

Volume of larger solid = Volume of smaller solid $\times$ Volume scale factor $V = 27 \times \frac{64}{27}$

Answer:

$64$ $\text{cm}^3$