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Planifying the lateral surface area of a cone, we get the ci

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Planifying the lateral surface area of a cone, we get the ci

by fskilnik@GMATH » Thu Feb 28, 2019 6:53 am

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GMATH practice exercise (Quant Class 11)

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Planifying the lateral surface area of a cone, we get the circular sector with center O and radius 18 shown in the figure. Which of the following is closest to the length of the height of this cone?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

Answer: [spoiler]____(C)__[/spoiler]
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by fskilnik@GMATH » Thu Feb 28, 2019 11:35 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 11)

Image

Planifying the lateral surface area of a cone, we get the circular sector with center O and radius 18 shown in the figure. Which of the following is closest to the length of the height of this cone?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Image

$$?\,\, \cong \,\,h$$
$${\text{circular}}\,\,{\text{base}}\,{\text{of}}\,\,{\text{cone}}\,\,:\,\,\,\,2\pi r\,\, = \,\,\frac{{{{160}^ \circ }}}{{{{360}^ \circ }}}\left( {2\pi \cdot 18} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,r = \frac{{16 \cdot 18}}{{36}} = 8$$
$$\left( {{\text{Pythagoras}}} \right)\,\,\,\,{h^2} = {18^2} - {8^2} = \underleftrightarrow {\left( {18 - 8} \right)\left( {18 + 8} \right)} = 260$$
$${h^2} \cong 256 = {16^2}\,\,\,\,\,\mathop \Rightarrow \limits^{h\, > \,\,0} \,\,\,\,\,? = 16$$


The correct answer is (C).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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