Answer:
B.
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
Please have a look at the attached photo.
My answer:
As given in the question, we know that:
The ratio of the area of the circle to the area of the square is π/4
- The formula to find the volume of the cone is:
V = 1/3*the height*the base area
<=> V1 = 1/3*h*π
- The formula to find the volume of the pyramid is:
V2 = 1/3*the height*the base area
<=> V = 1/3*h*4
=> the ratio of volume of the cone to the pyramid is:
= 
= (1/3*h*π
) / ( 1/3*h*4
)
= π/4
S we can conclude that the volume of the cone equals π/4 the volume of the pyramid
Hope it will find you well.
Answer:
okok I willl hel0 you out
Question:
Which expression is equivalent to
![\frac{\sqrt{2}}{\sqrt[3]{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D)
Answer:
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{1}{6}} = \sqrt[6]{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%3D%20%5Csqrt%5B6%5D%7B2%7D)
Step-by-step explanation:
Given
![\frac{\sqrt{2}}{\sqrt[3]{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D)
Required
Simplify
From laws of indices;
![\sqrt[n]{x} =x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3Dx%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
So, the expression can be rewritten as
![\frac{\sqrt{2}}{\sqrt[3]{2}} = \frac{{2^{\frac{1}{2}}}}{2^{\frac{1}{3}}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D%20%5Cfrac%7B%7B2%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7D%7B2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D)
Also, from laws of indices

So, the expression is further solved to:
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{1}{2} - \frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B1%7D%7B2%7D%20-%20%5Cfrac%7B1%7D%7B3%7D)
Solve exponents as fraction
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{3-2}{6}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B3-2%7D%7B6%7D%7D)
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{1}{6}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D)
This can be rewritten as
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{1}{6}} = \sqrt[6]{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%3D%20%5Csqrt%5B6%5D%7B2%7D)