All categories

3 years ago

Find the volume of a regular hexagonal prism with the height of 22 apothem of 16 and a side length of 8

Mathematics

1 answer:

OverLord2011 [107]3 years ago

8 0

Answer:

$V=8,448u^3$

Step-by-step explanation:

The volume of a prism is given by:

$V=A_{b}*h$

where $A_{b}$ is the area of the base, and $h$ is the height of thr prism.

We know that the height is:

$h=22$ u

and the bases of this prism are hexagons.

Thus the area of the base is the area of a regular hexagon:

$A_{b}=\frac{n*l*a}{2}$

where $n$ is the number of sides: for an hexagon: $n=6$

$l$ is the length of each side: $l=8$ u,

and $a$ is the apothem: $a=16u$

we substitute all of this to find the area of the base:

$A_{b}=\frac{6*8u*16u}{2}\\ \\A_{b}=\frac{768u^2}{2}\\ \\A_{b}=384u^2$

and finally we use the formula for the volume:

$V=A_{b}*h$

we get the following:

$V=384u^2*22u\\V=8,448u^3$

which is the third option

You might be interested in

Keisha is solving the equation 7^x=9.

olganol [36]

$\bf \textit{Logarithm of exponentials}\\\\
log_a\left( x^ b \right)\implies b\cdot log_a(x)\\\\
-------------------------------\\\\
7^x=9\implies \boxed{log(7^x)=log(9)}\implies x\cdot log(7)=log(9)
\\\\\\
x=\cfrac{log(9)}{log(7)}$

3 0

3 years ago

I REALLY NEED HELP QUICK!

Leni [432]

Answer:

y=1/2x-5

Step-by-step explanation:

From the picture you can see that (0, -5) is a point on the function and that (2, -4) is another point. Using these you can find the slope of the function with the equation

$(y_{2} -y_{1})/(x_{2}-x_{1} )$

We can substitute in the points so it looks like

$(-4--5)/(2-0)$ or $1/2$ which is the slope of the function

Now, since the y-intercept is (0, -5) on the graph, the b part in the slope-intercept form of the equation would be -5, leaving us with the equation y=1/2x-5

4 0

3 years ago

Can anyone help!<br> WITH STEPS!

MissTica

Answer:

When we have something like:

$\sqrt[n]{x}$

It is called the n-th root of x.

Where x is called the radicand, and n is called the index.

Then the term:

$\sqrt[4]{16}$

is called the fourth root of 16.

And in this case, we can see that the index is 4, and the radicand is 16.

At the end, we have the question: what is the 4th root of 16?

this is:

$\sqrt[4]{16} = \sqrt[4]{4*4} = \sqrt[4]{2*2*2*2} = 2$

The 4th root of 16 is equal to 2.

6 0

2 years ago

You plant a rectangular rose garden along the side of your garage. You enclose 3 sides of the garden with 40 feet of fencing. Th

solmaris [256]

Let's assume

length of rectangle =L

width of rectangle =W

You enclose 3 sides of the garden with 40 feet of fencing

so, we get

$L+2W=40$

now, we can solve for L

$L=40-2W$

we know that

area of rectangle is

$A=L*W$

$100=L*W$

now, we can plug

$100=(40-2W)*W$

now, we can solve for W

$-2W^2+40W-100=0$

we can use quadratic formula

$W=\frac{-40+\sqrt{40^2-4\left(-2\right)\left(-100\right)}}{2\left(-2\right)}$

$W=\frac{-40-\sqrt{40^2-4\left(-2\right)\left(-100\right)}}{2\left(-2\right)}$

we can take anyone value ..because both are giving positive value

first dimensions:

$W=2.929$

now, we can find L

$L=40-2*2.929$

$L=34.142$

so, length is 34.142feet

width is 2.929 feet

Second dimensions:

$W=17.071$

now, we can find L

$L=40-2*17.071$

$L=5.858$

so, length is 5.858feet

width is 17.071 feet

6 0

3 years ago

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first deter

VMariaS [17]

Answer:

He must survey 123 adults.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.