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2 years ago

How should I solve this? I tried to but I couldn't get past the quadratic formula.

Mathematics

1 answer:

xxMikexx [17]2 years ago

8 0

First multiply all terms by z
8-z^2=4z

Then order into standard form
-z^2-4z+8=0

Multiply the equation by -1
z^2+4z-8=0

Plug into quadratic equation
-4±√16-4(-8)
-4±√48

(-4±4√3)/2
-2±2√3

Final answer: z=-2± 2√3

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We are to find the volume of the pyramid.

The formula for finding the volume of a pyramid is given by

$V=\dfrac{1}{3}b\times h,$

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Here, b = 54√3 cm², h = ?

Now, from the right-angled triangle ABC, we have

$\dfrac{\textup{BC}}{\textup{AC}}=\tan 60^\circ\\\\\Rightarrow \dfrac{h}{6}=\sqrt 3\\\\\Rightarrow h=6\sqrt 3.$

Therefore, the volume of the pyramid is

$V=\dfrac{1}{3}b\times h=\dfrac{1}{3}\times 54\sqrt 3\times 6\sqrt 3=324.$

Thus, the required volume is $V=324~\textup{cm}^3.$ This makes (C) as the correct option.

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