(1/3) × the cone's volume = The cylinder's volume.
Step-by-step explanation:
Step 1:
The volume of any cone is obtained by multiplying 
with π, the square of the radius (
) and the height (
).
So the volume of the cone, 
.
Step 2:
The cylinder's volume is nearly the same as the cone but instead by multiplying we multiply with 1.
So the cylinder's volume is determined by multiplying π with the square of the radius of the cylinder () and the height of the cylinder ().
So the the cone's volume, 
.
Step 3:
Now we equate both the volumes to each other.
The cone's volume : The cylinder's volume = 
= 
.
So if we multiply the cone's volume with we will get the cylinder's volume with the same dimensions.
Answer:
0.9625
Step-by-step explanation:
Answer:
Recursive:
Explicit:
And the 20th term is 225.
Step-by-step explanation:
We have the sequence:
35, 45, 55, 65.
Notice that each subsequent term is 10 more than the previous term.
Therefore, our common difference is (+)10.
Recursive Rule:
The standard format for the recursive rule is:
Where a is the initial term and d is the common difference.
From our sequence, we know that a the initial term is 35.
And as determined, our common difference d is 10.
Substitute. Hence, our recursive rule is:
Explicit Rule:
The standard format for the explicit rule is:
Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:
Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:
Evaluate:
Hence, the 20th term is 225.
