The first circle has a diameter of 10 inches. A second circle has a diameter that is twice the diameter of the first circle. Wha
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The volume of the silo is 461.81 m³
Step-by-step explanation:
A barn silo, excluding the top, is a cylinder
- The silo is 7 m in diameter
- Its height is 12 m
We need to find the volume of the silo
∵ The silo is shaped a cylinder
∵ The volume of a cylinder = base area × height
∵ The base is shaped a circle
∵ Area a circle = π r², where r is the radius of the circle
∴ The volume of the silo = π r² × h
∵ The diameter of the silo = 7 m
∵ The radius of a circle is half the diameter
∴ The radius of the silo = × 7 = 3.5 m
∵ The height of the silo = 12 m
- Substitute the values of r and h in the rule of volume
∴ The volume of the silo = π (3.5)² × 12
∴ The volume of the silo = 147 π = 461.81 m³
The volume of the silo is 461.81 m³
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Part A:
Given parabola (1) to be
, and parabola (2) to be 
Notice that parabola (2) is stretched horizontally by a factor of 13 which is greater than 1. This means that parabola (2) is further away from the x-axis than parabola (1). (i.e. parabola (2) is more 'vertical' than parabola (1).
Therefore, parabola (1) is wider than parabola (2).
Part B:
A parabola open up when the coefficient of the quadratic term (the squared term) is positive and opens down when the coefficient of the quadratic term is negative.
Given parabola (1) to be, and parabola (2) to be
Notice that the coefficient of the quadratic term is positive for parabola (2) and negative for parabola (1), therefore, the parabola that will open down is parabola (1).
Part C:
For any function, f(x), the graph of the function is moved p places to the left when p is added to x (i.e. f(x + p)) and moves p places to the right when p is subtracted from x (i.e. f(x - p)).
Given parabola (1) to be, and parabola (2) to be
Notice that in parabola (1), 12 is added to x, which means that the graph of the parent function is shifted 12 places to the left while in parabola (2), 4 is subtracted from x, which means that the graph of the parent function is shifted 4 places to the right.
Therefore, the parabola that would be furthest left on the x-axis is parabola (1).
Part D:
For any function, f(x), the graph of the function is moved q places up when q is added to the function (i.e. f(x) + q) and moves q places down when q is subtracted from the function (i.e. f(x) - q).
Given parabola (1) to be, and parabola (2) to be
Notice that in parabola (2), 1 is added to the function, which means that the graph of the parent function is shifted 1 place up while in parabola (1), 6 is subtracted from the function, which means that the graph of the parent function is shifted 6 places down.
Therefore, the parabola that would be highest on the y-axis is parabola (2).
Given parabola (1) to be
Notice that parabola (2) is stretched horizontally by a factor of 13 which is greater than 1. This means that parabola (2) is further away from the x-axis than parabola (1). (i.e. parabola (2) is more 'vertical' than parabola (1).
Therefore, parabola (1) is wider than parabola (2).
Part B:
A parabola open up when the coefficient of the quadratic term (the squared term) is positive and opens down when the coefficient of the quadratic term is negative.
Given parabola (1) to be
Notice that the coefficient of the quadratic term is positive for parabola (2) and negative for parabola (1), therefore, the parabola that will open down is parabola (1).
Part C:
For any function, f(x), the graph of the function is moved p places to the left when p is added to x (i.e. f(x + p)) and moves p places to the right when p is subtracted from x (i.e. f(x - p)).
Given parabola (1) to be
Notice that in parabola (1), 12 is added to x, which means that the graph of the parent function is shifted 12 places to the left while in parabola (2), 4 is subtracted from x, which means that the graph of the parent function is shifted 4 places to the right.
Therefore, the parabola that would be furthest left on the x-axis is parabola (1).
Part D:
For any function, f(x), the graph of the function is moved q places up when q is added to the function (i.e. f(x) + q) and moves q places down when q is subtracted from the function (i.e. f(x) - q).
Given parabola (1) to be
Notice that in parabola (2), 1 is added to the function, which means that the graph of the parent function is shifted 1 place up while in parabola (1), 6 is subtracted from the function, which means that the graph of the parent function is shifted 6 places down.
Therefore, the parabola that would be highest on the y-axis is parabola (2).