7:53 PM \& 으 proyecto.webescuela.cl/siste 6 C) $$ \checkmark $$ 10 cm d) 20 cm Enviar 34) ¿Cuál es, aproximadamente, el volumen de un cono si el diámetro basal mide 18 cm y su altura $$ \mathbf{2 5} \mathbf{c m} $$ ? Usa $$ \pi \approx 3,14 $$. a) $$ 2120 \mathrm{~cm}^{3} $$ b) $$ 1413 \mathrm{~cm}^{3} $$ c) $$ 236 \mathrm{~cm}^{3} $$ d) $$ 8478 \mathrm{~cm}^{3} $$ Enviar 35) El volumen de un cono es $$ 18 \mathrm{~m}^{3} $$. ¿Cuál es el volumen de un cilindro con igual base y altura? a) $$ 6 \mathrm{~m}^{3} $$ b) $$ 18 \mathrm{~m}^{3} $$

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UpStudy AI · Accepted Answer

To solve the problems presented, we will follow these steps:

### Problem 34: Volume of a Cone

1. **Extract Known Conditions:**
   - Diameter of the base $$ d = 18 \, \text{cm} $$
   - Height $$ h = 25 \, \text{cm} $$
   - Use $$ \pi \approx 3.14 $$

2. **Calculate the Radius:**
   The radius $$ r $$ is half of the diameter:
   $$
   r = \frac{d}{2} = \frac{18}{2} = 9 \, \text{cm}
   $$

3. **Volume Formula for a Cone:**
   The volume $$ V $$ of a cone is given by the formula:
   $$
   V = \frac{1}{3} \pi r^2 h
   $$

4. **Substituting the Values:**
   Now we substitute $$ r $$ and $$ h $$ into the volume formula:
   $$
   V = \frac{1}{3} \cdot 3.14 \cdot (9)^2 \cdot 25
   $$

5. **Calculating the Volume:**
   First, calculate $$ (9)^2 $$:
   $$
   (9)^2 = 81
   $$
   Now substitute back into the volume formula:
   $$
   V = \frac{1}{3} \cdot 3.14 \cdot 81 \cdot 25
   $$

6. **Performing the Calculation:**
   Let's calculate $$ 81 \cdot 25 $$:
   $$
   81 \cdot 25 = 2025
   $$
   Now substitute this value:
   $$
   V = \frac{1}{3} \cdot 3.14 \cdot 2025
   $$

7. **Final Calculation:**
   Now calculate $$ 3.14 \cdot 2025 $$:
   $$
   3.14 \cdot 2025 = 6369.5
   $$
   Finally, divide by 3:
   $$
   V = \frac{6369.5}{3} \approx 2123.17 \, \text{cm}^3
   $$

8. **Choosing the Closest Option:**
   The closest option to $$ 2123.17 \, \text{cm}^3 $$ is:
   - a) $$ 2120 \, \text{cm}^3 $$

### Problem 35: Volume of a Cylinder

1. **Extract Known Conditions:**
   - Volume of the cone $$ V_{\text{cone}} = 18 \, \text{m}^3 $$

2. **Volume of a Cylinder with Equal Base and Height:**
   The volume $$ V_{\text{cylinder}} $$ of a cylinder with the same base and height as a cone is given by:
   $$
   V_{\text{cylinder}} = 3 \cdot V_{\text{cone}}
   $$

3. **Calculating the Volume of the Cylinder:**
   $$
   V_{\text{cylinder}} = 3 \cdot 18 = 54 \, \text{m}^3
   $$

4. **Choosing the Closest Option:**
   Since the options provided are:
   - a) $$ 6 \, \text{m}^3 $$
   - b) $$ 18 \, \text{m}^3 $$

The volume of the cylinder is not listed among the options, but it is clear that the volume of the cylinder is three times that of the cone.

### Final Answers:
- For Problem 34: **a) $$ 2120 \, \text{cm}^3 $$**
- For Problem 35: The volume of the cylinder is $$ 54 \, \text{m}^3 $$, which is not listed in the options.
- **Problem 34:** The volume of the cone is approximately $$ 2120 \, \text{cm}^3 $$. - **Problem 35:** The volume of the cylinder is $$ 54 \, \text{m}^3 $$.

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