MATH SOLVE

2 months ago

Q:
# A sphere and a cylinder have the same radius and height. The volume of the cylinder is . Amie found the volume of the sphere.

Accepted Solution

A:

Answer:The answer is the firstAmie should have multiplied 54 by 2/3Step-by-step explanation:* Lets start with the rule of the volume of each solid∵ Volume the sphere = 4/3 π r³∵ Volume the cylinder = π r² h∵ The radii and the heights of the sphere and the cylinder are equal∴ The ratio between there volumes are 4/3 π r³ : π r² h - Lets divide each part by π r²∴ 4/3 r : h∵ The height of the sphere = the diameter of it = 2r∴ The height of the cylinder = 2r∴ The ratio will be: 4/3 r : 2r- Now divide each part by 2r∵ (4/3)r ÷ 2r = 2/3∵ 2r ÷ 2r = 1∴ The ratio is 2/3 : 1 ∴ The volume of the sphere = 2/3 the volume of the cylinder∵ The volume of the cylinder = 54 m³∴ The volume of the sphere = 2/3 × 54 = 36 m³∴ The answer is Amie should have multiplied 54 by 2/3