Answer:
3 of the pyramids
Step-by-step explanation:
Given:
Hexagonal Prism
Hexagonal based pyramid
Required
How many of the pyramid will fill up the prism
To do this, we start by calculating the volumes of both shapes.
Let V1 be the volume of the hexagonal prism
![V_1 = \frac{3\sqrt{3}}{2}a^2h](https://tex.z-dn.net/?f=V_1%20%3D%20%5Cfrac%7B3%5Csqrt%7B3%7D%7D%7B2%7Da%5E2h)
Where: a = base and h = height
Let V2 be the volume of the hexagonal based pyramid
![V_2 = \frac{\sqrt{3}}{2}a^2h](https://tex.z-dn.net/?f=V_2%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7Da%5E2h)
Where: a = base and h = height
The number of the pyramid that can occupy the prism is calculated by dividing V1 by V2
![Number = \frac{V_1}{V_2}](https://tex.z-dn.net/?f=Number%20%3D%20%5Cfrac%7BV_1%7D%7BV_2%7D)
![Number = \frac{3\sqrt{3}}{2}a^2h /\frac{\sqrt{3}}{2}a^2h](https://tex.z-dn.net/?f=Number%20%3D%20%20%5Cfrac%7B3%5Csqrt%7B3%7D%7D%7B2%7Da%5E2h%20%2F%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7Da%5E2h)
Convert division to multiplication
![Number = \frac{3\sqrt{3}}{2}a^2h * \frac{2}{\sqrt{3}a^2h}](https://tex.z-dn.net/?f=Number%20%3D%20%20%5Cfrac%7B3%5Csqrt%7B3%7D%7D%7B2%7Da%5E2h%20%2A%20%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7Da%5E2h%7D)
![Number = \frac{3\sqrt{3}}{2} * \frac{2}{\sqrt{3}}](https://tex.z-dn.net/?f=Number%20%3D%20%20%5Cfrac%7B3%5Csqrt%7B3%7D%7D%7B2%7D%20%2A%20%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D)
![Number = \frac{3\sqrt{3}}{1} * \frac{1}{\sqrt{3}}](https://tex.z-dn.net/?f=Number%20%3D%20%20%5Cfrac%7B3%5Csqrt%7B3%7D%7D%7B1%7D%20%2A%20%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D)
![Number = \frac{3*1}{1} * \frac{1}{1}](https://tex.z-dn.net/?f=Number%20%3D%20%20%5Cfrac%7B3%2A1%7D%7B1%7D%20%2A%20%5Cfrac%7B1%7D%7B1%7D)
![Number = 3](https://tex.z-dn.net/?f=Number%20%3D%20%203)
1.Find the Lowest Common Denominator(LCD) of the fractions.
Rename the fractions to have the LCD.
Subtract the numerators of the fractions.
The difference will be the numerator and the LCD will be the denominator of the answer.
Simplify the Fraction.
Answer:
8.3 X 10^-10
Step-by-step explanation:
Since the exponent of the scientific notation is negative, move the decimal point
10
places to the left.
0.0000000083
Step-by-step explanation:
Hi ✌ now multiply $2.50×4=1000