The height and base radius of a cone are increased by a factor of 2 to create a similar cone. How is the slant height of the cone affected? The slant height of the larger cone is equal to the slant height of the smaller cone. The slant height of the larger cone is double the slant height of the smaller cone. The slant height of the larger cone is 4 times the slant height of the smaller cone. The slant height of the larger cone is 8 times the slant height of the smaller cone.

Question

Mathematics

Jaydon Schmitt

8 May, 07:46

The height and base radius of a cone are increased by a factor of 2 to create a similar cone. How is the slant height of the cone affected? The slant height of the larger cone is equal to the slant height of the smaller cone. The slant height of the larger cone is double the slant height of the smaller cone. The slant height of the larger cone is 4 times the slant height of the smaller cone. The slant height of the larger cone is 8 times the slant height of the smaller cone.

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Answers (1)

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Jack Bush · Answer 1

The slant height of a cone is given by:

l₁ = √ (r² + h²)

Substituting the doubled values:

l = √ ((2r) ² + (2h) ²)

l = √ (4r² + 4h²)

l₂ = 2√ (r² + h²)

Therefore,

l₂ = 2l₁

Therefore, the slant height of the larger cone is double the slant height of the smaller cone.