Answer:
Choice D
Step-by-step explanation:
The Cavalieri's principle states that if two or more solids have identical cross-sectional area as well as height, then the solids will have equal volume.
Therefore, the volumes of the cylinders are the same
Answer:
![\large{YES}\ \dfrac{BC}{YZ}=\dfrac{AC}{XY}=\dfrac{AB}{XZ}=\dfrac{2}{1}\\\\\text{and}\ \angle B\cong\angle Z,\ \angle C\cong\angle Y,\ \angle A\cong\angle X](https://tex.z-dn.net/?f=%5Clarge%7BYES%7D%5C%20%5Cdfrac%7BBC%7D%7BYZ%7D%3D%5Cdfrac%7BAC%7D%7BXY%7D%3D%5Cdfrac%7BAB%7D%7BXZ%7D%3D%5Cdfrac%7B2%7D%7B1%7D%5C%5C%5C%5C%5Ctext%7Band%7D%5C%20%5Cangle%20B%5Ccong%5Cangle%20Z%2C%5C%20%5Cangle%20C%5Ccong%5Cangle%20Y%2C%5C%20%5Cangle%20A%5Ccong%5Cangle%20X)
Step-by-step explanation:
![BC\to ZY\\AB\to XZ\\AC\to XY\\\angle A\to\angle X\\\angle B\to\angle Z\\\angle C\to\angle Y](https://tex.z-dn.net/?f=BC%5Cto%20ZY%5C%5CAB%5Cto%20XZ%5C%5CAC%5Cto%20XY%5C%5C%5Cangle%20A%5Cto%5Cangle%20X%5C%5C%5Cangle%20B%5Cto%5Cangle%20Z%5C%5C%5Cangle%20C%5Cto%5Cangle%20Y)
![\text{We have:}\\\\\triangle ABC:\ AB=20,\ BC=12,\ AC=18\\\triangle XZY:\ XZ=10,\ YZ=6,\ XY=9\\\\\text{check the ratio:}\\\\\dfrac{AB}{XZ}=\dfrac{20}{10}=2\\\\\dfrac{BC}{YZ}=\dfrac{12}{6}=2\\\\\dfrac{AC}{XY}=\dfrac{18}{9}=2\\\\\text{CORRECT :)}\\\\\angle B\cong\angle Z,\ \angle C\cong\angle Y\\\\\text{We know that: The sum of the acute angles in a right triangle is}\ 90^o.\\\\m\angle B+m\angle A=90^o\ \text{and}\ m\angle Z+m\angle X=90^o](https://tex.z-dn.net/?f=%5Ctext%7BWe%20have%3A%7D%5C%5C%5C%5C%5Ctriangle%20ABC%3A%5C%20AB%3D20%2C%5C%20BC%3D12%2C%5C%20AC%3D18%5C%5C%5Ctriangle%20XZY%3A%5C%20XZ%3D10%2C%5C%20YZ%3D6%2C%5C%20XY%3D9%5C%5C%5C%5C%5Ctext%7Bcheck%20the%20ratio%3A%7D%5C%5C%5C%5C%5Cdfrac%7BAB%7D%7BXZ%7D%3D%5Cdfrac%7B20%7D%7B10%7D%3D2%5C%5C%5C%5C%5Cdfrac%7BBC%7D%7BYZ%7D%3D%5Cdfrac%7B12%7D%7B6%7D%3D2%5C%5C%5C%5C%5Cdfrac%7BAC%7D%7BXY%7D%3D%5Cdfrac%7B18%7D%7B9%7D%3D2%5C%5C%5C%5C%5Ctext%7BCORRECT%20%3A%29%7D%5C%5C%5C%5C%5Cangle%20B%5Ccong%5Cangle%20Z%2C%5C%20%5Cangle%20C%5Ccong%5Cangle%20Y%5C%5C%5C%5C%5Ctext%7BWe%20know%20that%3A%20The%20sum%20of%20the%20acute%20angles%20in%20a%20right%20triangle%20is%7D%5C%2090%5Eo.%5C%5C%5C%5Cm%5Cangle%20B%2Bm%5Cangle%20A%3D90%5Eo%5C%20%5Ctext%7Band%7D%5C%20m%5Cangle%20Z%2Bm%5Cangle%20X%3D90%5Eo)
![\text{We know}\ m\angle B=m\angle Z\to \ m\angle A=m\angle X.\\\text{therefore}\ \angle A\cong\angle X](https://tex.z-dn.net/?f=%5Ctext%7BWe%20know%7D%5C%20m%5Cangle%20B%3Dm%5Cangle%20Z%5Cto%20%5C%20m%5Cangle%20A%3Dm%5Cangle%20X.%5C%5C%5Ctext%7Btherefore%7D%5C%20%5Cangle%20A%5Ccong%5Cangle%20X)
Answer:
-4
Step-by-step explanation:
Answer: 196pi in.^2
Step-by-step explanation:
Divide the diameter by two.
You would get 14, then square it, you would get 196.
Answer:
y - 4 = (4/3)(x - 1)
Step-by-step explanation:
point slope form is
y - y1 = m(x - x1)
m is the slope
(x1, y1) is a point on the line
----------------------------
for m = 4/3 and (x1, y1) = (1, 4)
y - 4 = (4/3)(x - 1)