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4 years ago

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A regular square pyramid has base edges of length 16 and its lateral faces are inclined 30° to the base of the pyramid. What is

the (1) height of the pyramid (2) volume of the pyramid?

1 answer:

Vlad1618 [11]4 years ago

4 0

Answer:

(1) 13.86 units.

(2) 1182.72 cubic units.

Step-by-step explanation:

Please find the attachment.

We have been given that a regular square pyramid has base edges of length 16 and its lateral faces are inclined 30° to the base of the pyramid.

(1) We can find height of pyramid using tan.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

The length of opposite side will half the length of square base.

$\frac{16}{2}=8$

$\text{tan}(30^{\circ})=\frac{8}{h}$

$h=\frac{8}{\text{tan}(30^{\circ})}$

$h=13.8564064605420367$

$h\approx 13.86$

Therefore, the height of the pyramid will be 13.86 units.

(2). We know that volume of pyramid is 1/3 the product of base area and height.

$V=\frac{1}{3}*bh$

$V=\frac{1}{3}*16*16*13.86$

$V=\frac{1}{3}*3548.16$

$V=1182.72$

Therefore, the volume of the pyramid would be 1182.72 cubic units.

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The expected value is given by this formula:

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Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Part a

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=16, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The expected value is given by this formula:

$E(X) = np=16*0.2=3.2$

Part b

For this case we want this probability:

$P(X=0)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And using this function we got:

$P(X=0)=(16C0)(0.2)^{0} (1-0.2)^{16-0}=0.02815$

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