The image depicts a sphere with a radius labeled as 3 meters. A dotted line represents the radius extending from the center of the sphere to its surface. This illustration is often used to explain the concept of the volume of a sphere in geometry. The formula for the volume of a sphere is (4/3)πr³, where 'r' is the radius. In this case, with a radius of 3 meters, the volume would be (4/3)π(3³) = 36π cubic meters. The image is likely used for educational purposes, possibly in a textbook or online resource explaining geometric concepts.
Responses
A 9π cubic meters9π cubic meters
B 30π cubic meters30π cubic meters
C 36π cubic meters36π cubic meters
D 72π cubic meters
1 answer
To find the volume of a sphere using the formula \( V = \frac{4}{3} \pi r^3 \), where \( r \) is the radius, we can substitute the given radius of 3 meters into the formula.
Calculate \( r^3 \): \[ r^3 = 3^3 = 27 \]
Substitute \( r^3 \) into the volume formula: \[ V = \frac{4}{3} \pi (27) \]
Multiply: \[ V = \frac{4}{3} \times 27 \pi = 36 \pi \]
Therefore, the volume of the sphere is \( 36\pi \) cubic meters.
The correct response is: C 36π cubic meters.
