I scream cone!

Geometry Level 3

A circle with diameter 27 894 mm is cut to remove a quarter portion of it to turn it into a cone.

If θ \theta is the angle between the axis of symmetry and the slant height of the cone, what is csc ⁡ θ \csc \theta ?

Note: It's the quarter circle that was turned into a cone.


The answer is 4.

Ir J by IR J , 21, Philippines

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1 solution

Ir J
Jul 6, 2018

The numerical value of the radius of the quarter circle is not actually important, let's just assume it to be R.

So we can say that the slant height is equal to R.

The circular bottom of the cone will have a circumference of R π 2 \frac{Rπ}{2} . So it's radius then is R 4 \frac{R}{4} .

csc θ = H y p o t e n u s e O p p o s i t e S i d e \frac{Hypotenuse}{Opposite Side} = R R 4 \frac{R}{\frac{R}{4}} = 4 \boxed{4}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The problem should specify that it's the small portion that is used. "it" can refer to the circle we started with just as easily. Please change the wording. Thank you.

Marta Reece - 2 years, 11 months ago

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