The volume of a sphere is ![\cfrac{4}{3}\ \pi r^3](https://tex.z-dn.net/?f=%20%5Ccfrac%7B4%7D%7B3%7D%5C%20%5Cpi%20r%5E3%20)
So, if the small sphere has radius
and the largest sphere has radius
, their volumes are
![V_1 = \cfrac{4}{3}\ \pi r^3,\quad V_2 = \cfrac{4}{3}\ \pi (2r)^3 = \cfrac{4}{3}\ \pi 8r^3](https://tex.z-dn.net/?f=%20V_1%20%3D%20%5Ccfrac%7B4%7D%7B3%7D%5C%20%5Cpi%20r%5E3%2C%5Cquad%20V_2%20%3D%20%5Ccfrac%7B4%7D%7B3%7D%5C%20%5Cpi%20%282r%29%5E3%20%3D%20%5Ccfrac%7B4%7D%7B3%7D%5C%20%5Cpi%208r%5E3%20)
So, their ratio is
![\cfrac{V_2}{V_1} = \cfrac{\frac{4}{3}\ \pi 8r^3}{\frac{4}{3}\ \pi r^3} = 8](https://tex.z-dn.net/?f=%20%5Ccfrac%7BV_2%7D%7BV_1%7D%20%3D%20%5Ccfrac%7B%5Cfrac%7B4%7D%7B3%7D%5C%20%5Cpi%208r%5E3%7D%7B%5Cfrac%7B4%7D%7B3%7D%5C%20%5Cpi%20r%5E3%7D%20%3D%208%20)
Answer:
(4x - 2)(x^2 + 5x)
4x^3 + 20x^2 - 2x^2 - 10x
4x^3 + 18x^2 - 10x
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
the area of the carpet that is blue is 45