Si la altura de una pirámide recta es de 3𝑐𝑚 y el área de su base es 10𝑐𝑚2 , entonces el volumen de dicha pirámide es:Grupo de opciones de respuesta20𝑐𝑚3

1. ### Break Down the Problem

We need to calculate the volume $V$ of a pyramid using the formula: $V = \frac{1}{3} \cdot \text{Área de la base} \cdot \text{Altura}$

2. ### Relevant Concepts

• Volume of a pyramid formula: $V = \frac{1}{3} \cdot B \cdot h$ where $B$ is the area of the base and $h$ is the height.

3. ### Analysis and Detail

Given:

• Altura $h = 3 \, \text{cm}$
• Área de la base $B = 10 \, \text{cm}^2$

Now we substitute the values into the volume formula: $V = \frac{1}{3} \cdot 10 \, \text{cm}^2 \cdot 3 \, \text{cm}$ Calculating the volume: $V = \frac{1}{3} \cdot 30 \, \text{cm}^3 = 10 \, \text{cm}^3$

4. ### Verify and Summarize

We re-verified the calculations:

• Area of the base is $10 \, \text{cm}^2$
• Height is $3 \, \text{cm}$
• The volume calculation shows $V = 10 \, \text{cm}^3$.

Final Answer

The volume of the pyramid is $10 \, \text{cm}^3$.