I think 20% srry just woke up
Answer:
<em>The volume of pyramid B is 64 times the volume of pyramid A.</em>
<em></em>
Step-by-step explanation:
Given:
Two square pyramids A and B.
Side Length of A,
12 inches
Height of A,
8 inches
Side Length of B,
48 inches
Height of B,
32 inches
To find:
How many times bigger is the volume of pyramid B than pyramid A?
OR
is how many times bigger than
?
Solution:
First of all, let us have a look at the formula for volume of a pyramid:
![V=\dfrac{1}{3} \times \text{Area of Base} \times \text{Height}](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%20%5Ctext%7BArea%20of%20Base%7D%20%5Ctimes%20%5Ctext%7BHeight%7D)
Here, base is square, so:
![V=\dfrac{1}{3} \times s^2 \times h](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%20s%5E2%20%5Ctimes%20h)
Volume of pyramid A:
![V_A=\dfrac{1}{3} \times s_A^2 \times h_A](https://tex.z-dn.net/?f=V_A%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%20s_A%5E2%20%5Ctimes%20h_A)
![\Rightarrow V_A=\dfrac{1}{3} \times 12^2 \times 8 = 384\ inch^3](https://tex.z-dn.net/?f=%5CRightarrow%20V_A%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%2012%5E2%20%5Ctimes%208%20%3D%20384%5C%20inch%5E3)
Volume of pyramid B:
![V_B=\dfrac{1}{3} \times s_B^2 \times h_B](https://tex.z-dn.net/?f=V_B%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%20s_B%5E2%20%5Ctimes%20h_B)
![\Rightarrow V_B=\dfrac{1}{3} \times 48^2 \times 32 \\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 4^2 \times 4\\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 64\\\Rightarrow V_B= 24576\ inch^3 = 384\times 64\ inch^3\\\Rightarrow V_B = V_A\times 64\ inch^3](https://tex.z-dn.net/?f=%5CRightarrow%20V_B%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%2048%5E2%20%5Ctimes%2032%20%5C%5C%5CRightarrow%20V_B%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%2012%5E2%20%5Ctimes%208%20%5Ctimes%204%5E2%20%5Ctimes%204%5C%5C%5CRightarrow%20V_B%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%2012%5E2%20%5Ctimes%208%20%5Ctimes%2064%5C%5C%5CRightarrow%20V_B%3D%2024576%5C%20inch%5E3%20%3D%20384%5Ctimes%2064%5C%20inch%5E3%5C%5C%5CRightarrow%20V_B%20%3D%20V_A%5Ctimes%2064%5C%20inch%5E3)
<em>The volume of pyramid B is 64 times the volume of pyramid A.</em>
The perimeter is 32
I'm having a little difficulty finding the area because I forgot how the get the height... if I knew the height I would tell you.
I am so sorry I can not help all the way.
but if you find the height Area= base (11) times height (?)
Answer: B
Step-by-step explanation:
∠a and ∠b are complementary angles. Complementary angles are two angles adjacent to each other that add up to 90°. We know this is true because of the 90° angle that is labelled.
Vertical angles are not adjacent to each other. They are across from each other, connected by the angle. They are equal in angles. It is clear that ∠a and ∠b are not equal in angles. Therefore, they are complementary angles.