A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inc
hes. Use π = 3.14. What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.
1 answer:
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PART A
The given equation is
In order to find the maximum height, we write the function in the vertex form.
We factor -16 out of the first two terms to get,
We add and subtract
to get,
We again factor -16 out of the first two terms to get,
This implies that,
The quadratic trinomial above is a perfect square.
This finally simplifies to,
The vertex of this function is
The y-value of the vertex is the maximum value.
Therefore the maximum value is,
PART B
When the ball hits the ground,
This implies that,
We add -29 to both sides to get,
This implies that,
or
Since time cannot be negative, we discard the negative value and pick,
The given equation is
In order to find the maximum height, we write the function in the vertex form.
We factor -16 out of the first two terms to get,
We add and subtract
to get,
We again factor -16 out of the first two terms to get,
This implies that,
The quadratic trinomial above is a perfect square.
This finally simplifies to,
The vertex of this function is
The y-value of the vertex is the maximum value.
Therefore the maximum value is,
PART B
When the ball hits the ground,
This implies that,
We add -29 to both sides to get,
This implies that,
or
Since time cannot be negative, we discard the negative value and pick,