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Question Number 176853 by Ar Brandon last updated on 27/Sep/22

	Answered by som(math1967) last updated on 27/Sep/22

	$\frac{P T}{T A} = \frac{P R}{R K} = \frac{P S}{S E} = \frac{2}{3}$ $l e t P T = P R = P S = 2 x$ $T A = 3 x$ $∴ e a c h s i d e o f c u b e = P T + T A = 5 x$ $v o l o f p y r a m i d = \frac{1}{3} \times a r △ P T S \times P R$ $= \frac{1}{3} \times \frac{1}{2} \times 2 x \times 2 x \times 2 x = \frac{4 x^{3}}{3}$ $v o l o f c u b e = {(5 x)}^{3} = 125 x^{3}$ $r a t i o o f v o l u m e o f t h e m$ $\frac{4 x^{3}}{3} : 125 x^{3}$ $4 : 375$
	Commented by Ar Brandon last updated on 27/Sep/22
	Thank you Sir
	Answered by mr W last updated on 27/Sep/22

	$3 \times P T = 2 \times T A$ $\Rightarrow \frac{P T}{P A} = \frac{2}{5}$ $s i m i l a r l y$ $\Rightarrow \frac{P R}{P K} = \frac{2}{5}, \frac{P S}{P E} = \frac{2}{5}$ $v o l u m e o f p y r a m i d = \frac{P T \times P R \times P S}{6}$ $v o l u m e o f c u b e = P A \times P K \times P E$ $\frac{v o l u m e o f p y r a m i d}{v o l u m e o f c u b e} = \frac{P T \times P R \times P S}{6 \times P A \times P K \times P E}$ $= \frac{1}{6} \times {(\frac{2}{5})}^{3} = \frac{4}{375}$
	Commented by Ar Brandon last updated on 27/Sep/22
	Thank you Sir!
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