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Which of the following formulas finds the lateral area of a right cone where [tex]\( r \)[/tex] is the radius and [tex]\( s \)[/tex] is the slant height?

A. [tex]\( LA = \frac{1}{2} \pi r s \)[/tex]
B. [tex]\( LA = r s \)[/tex]
C. [tex]\( LA = \pi r^2 + \pi r s \)[/tex]
D. [tex]\( LA = \pi r s \)[/tex]

Sagot :

GinnyAnswer
To find the lateral area of a right cone, we use the formula for the lateral area [tex]\( \text{LA} \)[/tex]. The correct formula is given by:

[tex]\[ \text{LA} = \pi r s \][/tex]

where:
- [tex]\( r \)[/tex] is the radius of the base of the cone.
- [tex]\( s \)[/tex] is the slant height of the cone.

Analyzing the given options:

Option A: [tex]\( \text{LA} = \frac{1}{2} \pi r s \)[/tex]

This is incorrect because the formula for the lateral area of a cone does not include the factor [tex]\(\frac{1}{2}\)[/tex].

Option B: [tex]\( \text{LA} = r s \)[/tex]

This is also incorrect because it lacks the [tex]\(\pi\)[/tex] factor. The complete formula must include [tex]\(\pi\)[/tex].

Option C: [tex]\( \text{LA} = \pi r^2 + \pi r s \)[/tex]

This formula adds the base area ([tex]\(\pi r^2\)[/tex]), which is not part of the lateral area. The lateral area should only account for the side surface area, not the base.

Option D: [tex]\( \text{LA} = \pi r s \)[/tex]

This is the correct formula for the lateral area of a right cone. It correctly incorporates both the radius [tex]\( r \)[/tex] and the slant height [tex]\( s \)[/tex] with the [tex]\(\pi\)[/tex] factor.

Therefore, the correct option is:

D. [tex]\( \text{LA} = \pi r s \)[/tex]
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