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. ACT/SAT Which of the following expressions represents the lateral area of the cone, in square inches, in terms of x? 6 in. x in. F πχνχ2 - 36 H σπα J π(x² - 36) K 2π(x²-36)​

ACTSAT Which of the following expressions represents the lateral area of the cone in square inches in terms of x 6 in x in F πχνχ2 36 H σπα J πx 36 K 2πx36 class=

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Intriguing456

Answer:

F. [tex]\pi x\sqrt{x^2-36}[/tex]

Step-by-step explanation:

The lateral area of a cone is given by the formula:

[tex]LA = \pi rh[/tex]

where:

  • [tex]r[/tex] is the radius of the base
  • [tex]h[/tex] is the lateral height

We are given the following dimension:

  • [tex]h = x[/tex]

We can solve for the radius of the base using the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

↓ plugging in the given values

[tex]6^2 + r^2 = x^2[/tex]

↓ subtracting 36 from both sides

[tex]r^2 = x^2-36[/tex]

↓ taking the square root of both sides

[tex]r=\sqrt{x^2-36}[/tex]

Finally, we can plug the known values into the formula:

[tex]\boxed{LA = \pi x\sqrt{x^2-36}}[/tex]

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