Simplify 3(x + 3) - 2x(x - 1) Evaluate 4½ x 4 Solve the equation (x − 1)2 − 25 = 0 Factorise 15 - 4x - 3x2

For similar solids, if the ratio of their corresponding lengths is $k$, then the ratio of their surface areas is $k^2$.
Given the ratio of surface areas of the smaller solid to the bigger solid is $4:25$.
Let $k$ be the ratio of corresponding lengths (smaller to bigger).

$$k^2 = \frac{4}{25}$$

To find $k$, take the square root of both sides:

$$k = \sqrt{\frac{4}{25}} = \frac{\sqrt{4}}{\sqrt{25}} = \frac{2}{5}$$

For similar solids, if the ratio of their corresponding lengths is $k$, then the ratio of their volumes is $k^3$.
Using the value of $k$ from Step 1, the ratio of the volumes (smaller to bigger) is:

$$k^3 = \left(\frac{2}{5}\right)^3 = \frac{2^3}{5^3} = \frac{8}{125}$$

Let $V_S$ be the volume of the smaller solid and $V_B$ be the volume of the bigger solid.
We have the ratio $\frac{V_S}{V_B} = \frac{8}{125}$.
Given that the volume of the bigger solid $V_B = 62.5 \text{ cm}^3$.
Now, substitute the value of $V_B$ into the ratio equation:

$$\frac{V_S}{62.5 \text{ cm}^3} = \frac{8}{125}$$ $$V_S = \frac{8}{125} \times 62.5 \text{ cm}^3$$ $$V_S = 8 \times \frac{62.5}{125} \text{ cm}^3$$ $$V_S = 8 \times 0.5 \text{ cm}^3$$ $$V_S = \boxed{4 \text{ cm}^3}$$