Question

lista de exercícios - prismas - prof. marco aurélio

1. calcule a área total da superfície e o volume dos prismas abaixo

a)

(image of a cube with edge length 5 cm)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"tutor"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Cube Surface Area",
"Cube Volume"
],
"current_concepts": [
"Cube Surface Area",
"Cube Volume",
"Prisms"
]
}
</pre_analysis>

<reasoning>

Identify the given dimensions

The figure shows a cube with an edge length of \(s = 5\text{ cm}\).

Calculate the base area

The base is a square.
\[
A_b = s^2 = 5^2 = 25\text{ cm}^2
\]

Calculate the total surface area

A cube has six identical square faces.
\[
A_t = 6 \cdot s^2 = 6 \cdot 25 = 150\text{ cm}^2
\]

Calculate the volume

The volume of a cube is the edge length cubed.
\[
V = s^3 = 5^3 = 125\text{ cm}^3
\]
</reasoning>

<answer>
Total Surface Area: \(150\text{ cm}^2\)
Volume: \(125\text{ cm}^3\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Geometry",
"Cube Surface Area"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"tutor"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Cube Surface Area",
"Cube Volume"
],
"current_concepts": [
"Cube Surface Area",
"Cube Volume",
"Prisms"
]
}
</pre_analysis>

<reasoning>

Identify the given dimensions

The figure shows a cube with an edge length of \(s = 5\text{ cm}\).

Calculate the base area

The base is a square.
\[
A_b = s^2 = 5^2 = 25\text{ cm}^2
\]

Calculate the total surface area

A cube has six identical square faces.
\[
A_t = 6 \cdot s^2 = 6 \cdot 25 = 150\text{ cm}^2
\]

Calculate the volume

The volume of a cube is the edge length cubed.
\[
V = s^3 = 5^3 = 125\text{ cm}^3
\]
</reasoning>

<answer>
Total Surface Area: \(150\text{ cm}^2\)
Volume: \(125\text{ cm}^3\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Geometry",
"Cube Surface Area"
]
}
</post_analysis>