Final answer:
The volume of a sphere with a diameter of 6.4 cm is found using the formula V = ⅓πr³, where the radius is 3.2 cm. This gives a volume of approximately 137.258 cm³, which rounds to 137.3 cm³ to the nearest tenth.
Step-by-step explanation:
To calculate the volume of a sphere, the formula V = ⅓πr³ is used, where V is volume, π (pi) is approximately 3.14159, and r is the radius of the sphere. First, we need to find the radius by halving the diameter. For a sphere with a diameter of 6.4 cm, the radius r is 3.2 cm. Then we substitute the radius into the formula:
V = ⅓π(3.2 cm)³
V = ⅓ x 3.14159 x (3.2 cm x 3.2 cm x 3.2 cm)
V = ⅓ x 3.14159 x 32.768 cm³
V = ⅓ x 3.14159 x 32.768 cm³
V = 137.258 cm³ (before rounding)
When rounded to the nearest tenth of a cubic centimeter, the volume of the sphere is approximately 137.3 cm³.