The square piece of wood measures 32 in per side,
Then the circle that can be cut off it has a radius of 16 in (half of the diameter 32 in)
Therefore, the area of the circle is going to be given by the formula:
And the area of the initial square was:
Area = 32^2 in^2 = 1024 in^2
Therefore the left-overs of the piece of wood would be the difference:
1024 in^2 - 803.84 in^2
Answer:
vertex = (- 1, - 4.5 )
Step-by-step explanation:
Given
f(x) = (x - 2)(x + 4)
The vertex lies on the axis of symmetry which is positioned at the midpoint of the zeros.
To find the zeros let f(x) = 0, that is
(x - 2)(x + 4) = 0
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x + 4 = 0 ⇒ x = - 4
The x- coordinate of the vertex is therefore
x = =
= - 1
Substitute x = - 1 into f(x) for corresponding y- coordinate
f(- 1) = (- 1 - 2)(- 1 + 4) =
× - 3 × 3 = 0.5 × - 9 = - 4.5
Coordinates of vertex = (- 1, - 4.5 )
<u>Given</u>:
The volume of a cylinder is cubic units.
A cone shares the same base.
The height of the cone is twice the height of the cylinder.
We need to determine the volume of the cone.
<u>Height of the Cone:</u>
Let h denote the height of the cylinder.
Let H denote the height of the cone.
Since, it is given that, the height of the cone is twice the height of the cylinder, we have;
<u>Volume of the cylinder:</u>
The formula to determine the volume of the cylinder is
Since, volume of the cylinder is , we get;
-------(1)
<u>Volume of the cone:</u>
The formula to determine the volume of the cone is
Substituting , we get;
Substituting equation (1), we get;
Thus, the volume of the cone is 20π
Hence, Option C is the correct answer.