Answer:
The capacity of the container is 2546.78 cm³.
Step-by-step explanation:
The volume of the frustum of a cone is:
![\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}]](https://tex.z-dn.net/?f=%5Ctext%7BVolume%7D%3D%5Cfrac%7B%5Cpi%20h%7D%7B3%7D%5Ccdot%5BR%5E%7B2%7D%2BRr%2Br%5E%7B2%7D%5D)
The information provided is:
r = 16/2 = 8 cm
R = 24/2 = 12 cm
h = 8 cm
Compute the capacity of the container as follows:
![\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}]](https://tex.z-dn.net/?f=%5Ctext%7BVolume%7D%3D%5Cfrac%7B%5Cpi%20h%7D%7B3%7D%5Ccdot%5BR%5E%7B2%7D%2BRr%2Br%5E%7B2%7D%5D)
![=\frac{\pi\cdot8}{3}\cdot[(12)^{2}+(12\cdot 8)+(8)^{2}]\\\\=\frac{8\pi}{3}\times [144+96+64]\\\\=\frac{8\pi}{3}\times304\\\\=2546.784445\\\\\approx 2546.78](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cpi%5Ccdot8%7D%7B3%7D%5Ccdot%5B%2812%29%5E%7B2%7D%2B%2812%5Ccdot%208%29%2B%288%29%5E%7B2%7D%5D%5C%5C%5C%5C%3D%5Cfrac%7B8%5Cpi%7D%7B3%7D%5Ctimes%20%5B144%2B96%2B64%5D%5C%5C%5C%5C%3D%5Cfrac%7B8%5Cpi%7D%7B3%7D%5Ctimes304%5C%5C%5C%5C%3D2546.784445%5C%5C%5C%5C%5Capprox%202546.78)
Thus, the capacity of the container is 2546.78 cm³.
Answer:
x= -6
Step-by-step explanation:
2(x+5)=x+4 (given)
2x+10=x+4 (distribute)
x+10=4 (simplify)
x= -6 (simplify again)
Answer:
The coordinates of point M' are
.
Step-by-step explanation:
According to the statement, we have the following translation rule:
(1)
Where:
- Original point.
- Translated point.
- Translation vector.
If we know that
, then the coordinates of the point M' are:


The coordinates of point M' are
.
Mandy: $16.25
Jermey: $16.25 + $3.40 = $19.65
Lily: $19.65 x 2 = $39.30
For Lily you would take the total of Jermey and times it by 2.