Math Problem Statement
A soap company changes the design of its soap from a cone to a sphere. The cone had a height of 3 centimeters (cm) and a radius of 2 cm . The
sphere has a diameter of 3 cm. The new design contains pi/f
centimeters more soap than the old design. What is the value of f?
Solution
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume of Solids
Equations
Formulas
Volume of a cone: V = (1/3)πr²h
Volume of a sphere: V = (4/3)πr³
Equation setup: V_sphere = V_cone + (π/f)
Theorems
Formula for volume of cone
Formula for volume of sphere
Suitable Grade Level
Grades 9-10
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