Carrillo Sanders
03/30/2023 · Elementary School
La relación entre el radio \( r \) de una esfera y su área total \( A \) es \( r=\left(\frac{A}{4 \pi}\right)^{\frac{1}{2}} \cdot \) ¿Cuál es el radio de una esfera que tiene un área total de \( 64 \pi \) unidades cuadradas?
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Tutor-Verified Answer
Step-by-step Solution
Para encontrar el radio \( r \) de una esfera con un área total \( A = 64 \pi \) unidades cuadradas, utilizamos la relación dada:
\[
r = \left(\frac{A}{4 \pi}\right)^{\frac{1}{2}}
\]
Sustituyendo \( A \) en la fórmula:
\[
r = \left(\frac{64 \pi}{4 \pi}\right)^{\frac{1}{2}}
\]
Simplificamos la fracción:
\[
r = \left(\frac{64}{4}\right)^{\frac{1}{2}} = \left(16\right)^{\frac{1}{2}}
\]
Calculamos la raíz cuadrada:
\[
r = 4
\]
Por lo tanto, el radio de la esfera es \( r = 4 \) unidades.
Quick Answer
El radio de la esfera es \( r = 4 \) unidades.
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