1. **State the problem:** (a) Solve for $r$ in the equation $$4 \pi r^3 = 45$$ (b) Simplify the expression $$\frac{45}{2}$$ and evaluate $$\sqrt{\frac{45}{2}}$$, then calculate $$\sqrt{12.745} \times 0.654$$ and add $$0.0653 + 40.53$$. --- 2. **Solve part (a):** Given $$4 \pi r^3 = 45$$, to find $r$, divide both sides by $4 \pi$: $$r^3 = \frac{45}{4 \pi}$$ Then take the cube root of both sides: $$r = \sqrt[3]{\frac{45}{4 \pi}}$$ Calculate the value inside the cube root: $$\frac{45}{4 \pi} \approx \frac{45}{12.566} \approx 3.58$$ Now find the cube root: $$r \approx \sqrt[3]{3.58} \approx 1.53$$ So, $$r \approx 1.53$$ units. --- 3. **Solve part (b):** First, simplify $$\frac{45}{2} = 22.5$$. Next, evaluate $$\sqrt{\frac{45}{2}} = \sqrt{22.5} \approx 4.74$$. Then calculate $$\sqrt{12.745} \times 0.654$$: $$\sqrt{12.745} \approx 3.57$$ Multiply: $$3.57 \times 0.654 \approx 2.33$$ Finally, add $$0.0653 + 40.53 = 40.5953$$. --- **Final answers:** (a) $$r \approx 1.53$$ (b) $$\frac{45}{2} = 22.5$$, $$\sqrt{\frac{45}{2}} \approx 4.74$$, $$\sqrt{12.745} \times 0.654 \approx 2.33$$, and $$0.0653 + 40.53 = 40.5953$$.