Given a cube with a volume of 27 cm³ what is the volume of a square piramid that can fit perfectly inside the cube?

Mathematics

1 answer:

Hunter-Best [27]3 years ago

5 0

As you know, a cube has all equal dimensions, thus length=width=height = x, check the picture below.

that means the square pyramid has a base of a 3x3 square, and its height is also 3, thus

$\bf \textit{volume of a pyramid}\\\\
V=\cfrac{1}{3}Bh~~
\begin{cases}
B=area~of\\
\qquad its~base\\
h=height\\
------\\
B=\stackrel{3\times 3}{9}\\
h=3
\end{cases}\implies V=\cfrac{1}{3}(9)(3)$

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borishaifa [10]

Answer:

a) $P(5$

And we can find this probability with this difference:

$P(-1.90$

And using the norma standard distribution or excel we got:

$P(-1.90$

b) $P(X>6) =P(Z> \frac{6-7.37}{1.25}) = P(Z>-1.096)$

And using the complement rule we got:

$P(Z>-1.096) =1-P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(7.37,1.25)$