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 :
(four decimal places)
Answer. Radius of the bottom of the hot tub (two decimal place
Check

Ask by Cummings Clarke. in Finland

Jan 02,2025

Question

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 :
(four decimal places)
Answer. Radius of the bottom of the hot tub (two decimal place
Check

Ask by Cummings Clarke. in Finland

Jan 02,2025

UpStudy AI · Accepted Answer

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 $$ \mathrm{r} = 0.78 \mathrm{m} $$
Radius of the bottom of the hot tub $$ \mathrm{r} = 0.78 \mathrm{m} $$

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 :
(four decimal places)
Answer. Radius of the bottom of the hot tub (two decimal place
Check

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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 : (four decimal places) Answer. Radius of the bottom of the hot tub (two decimal place Check

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Responder

Solución

The Deep Dive

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Latest Geometry Questions

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 :
(four decimal places)
Answer. Radius of the bottom of the hot tub (two decimal place
Check