5
QuizMultiple Choice

N/A — Exam

Question 5 • Algebraic Reasoning

The table shows the functions representing the height and base of a cone for different values of x x Height f of x is equal to 2 x Area of Base g of x is equal to pi x squared 1 2 pi 2 4 4 pi 3 6 9 pi 4 8 16 pi The volume of the cone when x is equal to 3 is 18 pi Which equation can be used to represent the volume of the cone, cap v times x ?

Answer
A
cap v times x is equal to 3 open paren f plus g close paren x
B
cap v times x is equal to 1 third open paren f plus g close paren x
C
cap v times x is equal to 1 third open paren f times g close paren x
D
cap v times x is equal to 3 open paren f times g close paren x

Explanation

A cone’s volume is one-third its base area times its height. Here, the height is f(x) and the base area is g(x), so V(x) = 1/3 · f(x)g(x). At x = 3, this gives 1/3 · 6 · 9π = 18π, matching the stated volume. Therefore, the equation is one-third of the product of f and g.

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