I think that 9 does not belong because 9 is a one dig it number and 25 43 and 16 are two dig it number. Also 25,43,16 are even but 9 is odd i hope this helps you and i hope it is right
Answer:
Often
Step-by-step explanation:
Hope this helps :D
This is a tricky question to answer without diagrams and there are useful videos online. A regular triangular prism has an equilateral triangle as its base with edge length 7cm, forming a prism with a total height of 11cm. We wish to calculate the area of the 3 equal triangular faces.
The formula for area of a triangle is 0.5 x base x height. We have the base (7cm) but the problem is we do not have the height (or slant length) of the lateral faces, we only have the height of the entire prism. We must first calculate the slant length by building a triangle inside the prism which goes from the centroid of the base (the inradius) to the centre of an edge. As the base is an equilateral triangle finding the inradius is much more difficult than for a square pyramid.
inradius = 1/6 x (SQRT of 3) x length
inradius = 1/6 x (SQRT of 3) x 7cm = 2cm
We now have a right angle triangle with base = inradius, height = height of prism, and hypotenuse = slant length we need.
Use pythag to calculate hypotenuse a^2 + b^2 = c^2
2^2 + 11^2 = c^2
4 + 121 = c^2
c= SQRT(125) = 11.18cm
We now have the missing slant length or height of the lateral triangles of the prism. We can find the area of one face and multiply it by 3 to get the total surface area of the lateral faces of the pyramid.
base = 7cm
height = 11.18cm
area of triangle = 0.5 x 7 x 11.18 = 39.13cm^2
Multiply this area by 3 to get the sum of all 3 lateral triangle surface areas, total area = 117.39cm^2
To solve this we are going to use the formula for the volume of a sphere:
![V= \frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=V%3D%20%5Cfrac%7B4%7D%7B3%7D%20%20%5Cpi%20r%5E3)
where
![r](https://tex.z-dn.net/?f=r)
is the radius of the sphere
Remember that the radius of a sphere is half its diameter; since the first radius of our sphere is 24 cm,
![r= \frac{24}{2} =12](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B24%7D%7B2%7D%20%3D12)
. Lets replace that in our formula:
![V= \frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=V%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
![V= \frac{4}{3} \pi (12)^3](https://tex.z-dn.net/?f=V%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2812%29%5E3)
![V=7238.23 cm^3](https://tex.z-dn.net/?f=V%3D7238.23%20cm%5E3)
Now, the second diameter of our sphere is 36, so its radius will be:
![r= \frac{36}{2} =18](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B36%7D%7B2%7D%20%3D18)
. Lets replace that value in our formula one more time:
![V= \frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=V%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
![V= \frac{4}{3} \pi (18)^3](https://tex.z-dn.net/?f=V%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2818%29%5E3)
![V=24429.02](https://tex.z-dn.net/?f=V%3D24429.02)
To find the volume of the additional helium, we are going to subtract the volumes:
Volume of helium=
![24429.02cm^3-7238.23cm^3=17190.79cm^3](https://tex.z-dn.net/?f=24429.02cm%5E3-7238.23cm%5E3%3D17190.79cm%5E3)
We can conclude that the volume of additional helium in the balloon is
approximately <span>
17,194 cm³.</span>
The shape would be a parallelogram.
Parallelograms have four sides, making them a quadrilateral. Also, opposite angles in a parallelogram are congruent (135 = 135 and 45 = 45).