Answer:
160 cubic centimeters
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
Let
z ---> the scale factor
----> the ratio of corresponding radii
simplify
![z=\frac{2}{3}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B2%7D%7B3%7D)
step 2
Find the volume of the smaller cone
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z ---> the scale factor
x ----> the volume of the smaller cone
y ---> the volume of the larger cone
![z^{3}=\frac{x}{y}](https://tex.z-dn.net/?f=z%5E%7B3%7D%3D%5Cfrac%7Bx%7D%7By%7D)
we have
![z=\frac{2}{3}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B2%7D%7B3%7D)
![y=540\ cm^3](https://tex.z-dn.net/?f=y%3D540%5C%20cm%5E3)
substitute
![(\frac{2}{3})^{3}=\frac{x}{540}](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B3%7D%3D%5Cfrac%7Bx%7D%7B540%7D)
![x=540(\frac{2}{3})^{3}](https://tex.z-dn.net/?f=x%3D540%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B3%7D)
![x=160\ cm^3](https://tex.z-dn.net/?f=x%3D160%5C%20cm%5E3)
Answer:
Volume of pyramid with square base is 1057.54 m³
Step-by-step explanation:
We are given:
Length of base of pyramid = 14.4 m
Height of pyramid = 15.3 m
We need to find:
Volume of pyramid with square base
The formula used is: ![Volume=\frac{1}{3}\times a^2 \times h](https://tex.z-dn.net/?f=Volume%3D%5Cfrac%7B1%7D%7B3%7D%5Ctimes%20a%5E2%20%5Ctimes%20h)
Where a = base of pyramid and h is height
Putting values and finding volume
![Volume=\frac{1}{3}\times a^2 \times h\\Volume=\frac{1}{3}\times (14.4)^2 \times (15.3)\\Volume=\frac{1}{3}\times 207.36 \times 15.3\\Volume=1057.54 \ m^3](https://tex.z-dn.net/?f=Volume%3D%5Cfrac%7B1%7D%7B3%7D%5Ctimes%20a%5E2%20%5Ctimes%20h%5C%5CVolume%3D%5Cfrac%7B1%7D%7B3%7D%5Ctimes%20%2814.4%29%5E2%20%5Ctimes%20%2815.3%29%5C%5CVolume%3D%5Cfrac%7B1%7D%7B3%7D%5Ctimes%20207.36%20%5Ctimes%2015.3%5C%5CVolume%3D1057.54%20%5C%20m%5E3)
So, Volume of pyramid with square base is 1057.54 m³
Answer:
7/3y
Step-by-step explanation:
5x + 9y = 10
-x +2=7/3y
1. Check the picture attached. Consider the half of the 8-sided die, that is the pyramid ABCDE:
2. The perimeter of the base is 6, so each side of the base is 6/4=3/2
3. The distance between the tallest points is 2 cm, si the height of Pyramid ABCDE is 1 cm.
4. Consider the right triangle EOM in the figure:
EO=1, OM= 3/4 (it is half of AB=3/2) and EM is the hypothenuse, so by the pythagorean theorem length of EM is
![\sqrt{1+ ( \frac{3}{4} )^{2} }= \sqrt{1+ \frac{9}{16} }= \sqrt{ \frac{25}{16} }= \frac{5}{4}](https://tex.z-dn.net/?f=%20%5Csqrt%7B1%2B%20%28%20%5Cfrac%7B3%7D%7B4%7D%20%29%5E%7B2%7D%20%7D%3D%20%20%5Csqrt%7B1%2B%20%5Cfrac%7B9%7D%7B16%7D%20%7D%3D%20%5Csqrt%7B%20%5Cfrac%7B25%7D%7B16%7D%20%7D%3D%20%5Cfrac%7B5%7D%7B4%7D%20%20)
(cm)
5. So side EBC has area
![\frac{1}{2}BC*EM= \frac{1}{2}* \frac{3}{2}* \frac{5}{4}= \frac{15}{16}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7DBC%2AEM%3D%20%20%5Cfrac%7B1%7D%7B2%7D%2A%20%5Cfrac%7B3%7D%7B2%7D%2A%20%5Cfrac%7B5%7D%7B4%7D%3D%20%5Cfrac%7B15%7D%7B16%7D%20%20)
6. The total area is 8*Area(EBC)=