How many spherical solid marbles, each having a radius of 0.3 cm, can be made from a solid sphere having a radius of 6 cm?

Explanation

The volume of a sphere is given by the formula: V = (4/3)πr³ Step 1: Calculate the volume of the larger sphere (radius = 6 cm). Let the radius of the larger sphere, R = 6 cm. Using the formula: Vlarge = (4/3)πR³ Vlarge = (4/3)π(6)³ Vlarge = (4/3)π(216) Vlarge = 288π cm³ Step 2: Calculate the volume of a small marble (radius = 0.3 cm). Let the radius of each small marble, r = 0.3 cm. Using the formula: Vsmall = (4/3)πr³ Vsmall = (4/3)π(0.3)³ Vsmall = (4/3)π(0.027) Vsmall = 0.036π cm³ Step 3: Find the number of small marbles that can be made. Number of small marbles = Vlarge / Vsmall = 288π / 0.036π = 288 / 0.036 = 8000 Answer: 8000 small marbles can be made from the larger sphere.