3
ALMultiple Choice

Volume of Spheres and Cones

Question 3 • Mathematical Models with Applications - MA4072 CR

Compare the quantity in column A with the quantity in column B. Choose the best answer.Column AColumn BThe volume of a cone with base radius = 4 in. and height = 5 in.The volume of a cone with base radius = 5 in. and height = 4 in.

Answer
A
The volume in Column A cone is larger.
B
The volume in Coulmn B cone is larger.
C
The two quantities are equal.
D
The relationship cannot be determined from the information given.

Explanation

The volume of a cone is V = (1/3)πr²h. For Column A, r²h = 4² × 5 = 80; for Column B, r²h = 5² × 4 = 100. Since the common factor (1/3)π is the same, Column B’s cone has the larger volume.

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