Question

Select the correct answer from each drop-down menu. The volume of a sphere whose diameter is 18 centimeters is π cubic centimeters. If its diameter were reduced by half, its volume would be of its original volume.

Answer 1

The volume of a sphere with an 18 cm diameter is ⅔π(9 cm)³. When the diameter is reduced by half, the volume becomes ⅔π(4.5 cm)³ which is ⅘ or 12.5% of the original volume.

Step-by-step explanation:

The question pertains to the volume of a sphere with a given diameter and the comparative volume when that diameter is reduced by half. The formula for the volume of a sphere is V = ⅔πr³, where 'r' is the radius of the sphere. If the diameter is 18 centimeters, which makes the radius 9 centimeters, the original volume is ⅔π(9 cm)³ = 3053.628π cm³.

When the diameter is reduced by half, the new diameter is 9 centimeters, and the radius is 4.5 centimeters. The new volume is ⅔π(4.5 cm)³ = 381.703π cm³. To find the ratio of the new volume to the original volume, we divide the new volume by the original volume, thus (381.703π cm³) / (3053.628π cm³) = ⅘ or 0.125. Therefore, the reduced sphere's volume is ⅘ or 12.5% of the original volume.