The volume of the hot tub is 2,300 liters and the height is 1.2 m . What is the radius of the bottom of the tub? First, calculate the area of the bottom of the tub as an intermediate result : \( \mathrm{A}= \) (four decimal places) Answer. Radius of the bottom of the hot tub \( \mathrm{r}=\square \mathrm{m} \) (two decimal place Check

To determine the radius of the bottom of the hot tub, we'll follow these steps: 1. **Convert Volume to Cubic Meters** The volume of the hot tub is given in liters, and we need to convert it to cubic meters since the height is in meters. \[ \text{Volume} (V) = 2{,}300 \text{ liters} \] \[ 1 \text{ cubic meter} = 1{,}000 \text{ liters} \] \[ V = \frac{2{,}300 \text{ liters}}{1{,}000} = 2.3 \text{ m}^3 \] 2. **Calculate the Area of the Bottom of the Tub** The volume \( V \) of a cylinder is related to the area \( A \) of its base and its height \( h \) by the formula: \[ V = A \times h \] Solving for \( A \): \[ A = \frac{V}{h} = \frac{2.3 \text{ m}^3}{1.2 \text{ m}} = 1.916666\ldots \text{ m}^2 \] Rounded to four decimal places: \[ \mathrm{A} = 1.9167 \text{ m}^2 \] 3. **Calculate the Radius of the Bottom of the Tub** The area \( A \) of a circle is related to its radius \( r \) by the formula: \[ A = \pi r^2 \] Solving for \( r \): \[ r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{1.9167}{3.1416}} \approx \sqrt{0.610} \approx 0.781 \text{ m} \] Rounded to two decimal places: \[ \mathrm{r} = 0.78 \text{ m} \] **Final Answer:** Radius of the bottom of the hot tub \( \mathrm{r} = 0.78 \mathrm{m} \)