Question
What is the volume of a sphere with a radius of 9.1 ft , rounded to the nearest tenth of a cubic foot?
Ask by Hart Savage. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
El volumen de la esfera con un radio de 9.1 pies es aproximadamente **3152.4 pies cúbicos**.
Solution
El volumen de una esfera con un radio de 9.1 pies es aproximadamente **3152.4 pies cúbicos**.
**Cálculo detallado:**
La fórmula para el volumen \( V \) de una esfera es:
\[
V = \frac{4}{3} \pi r^3
\]
Donde:
- \( r \) es el radio de la esfera.
- \( \pi \) es una constante aproximada a 3.1416.
Sustituyendo el valor del radio:
\[
V = \frac{4}{3} \times 3.1416 \times (9.1)^3
\]
Calculando \( 9.1^3 \):
\[
9.1^3 = 9.1 \times 9.1 \times 9.1 = 752.571 \, \text{pies cúbicos}
\]
Ahora, multiplicamos por \( \frac{4}{3} \pi \):
\[
V \approx \frac{4}{3} \times 3.1416 \times 752.571 \approx 3152.4 \, \text{pies cúbicos}
\]
Por lo tanto, el volumen de la esfera es aproximadamente **3152.4 pies cúbicos**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the volume of a sphere, you can use the formula \( V = \frac{4}{3} \pi r^3 \). Plugging in the radius of 9.1 ft, you calculate \( V = \frac{4}{3} \pi (9.1)^3 \). This will give you a volume of approximately 3056.9 cubic feet when rounded to the nearest tenth. Fun fact: The concept of a sphere has been known since ancient times, with mathematicians like Archimedes in the 3rd century BC studying its properties. He was so fascinated that he famously claimed the sphere has the greatest volume-to-surface area ratio of any three-dimensional shape, making it a champion among geometric forms!
