Question 1:
For this case we have that by definition, the area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
r: It is the radius of the circle.
They tell us that the diameter is 9 inches, then the radius is 4.5 inches. substituting we have:
[tex]A = \pi * (4.5) ^ 2\\A = \pi * 20.25\\A = 63.59[/tex]
Thus, the area of the circle is[tex]63.59 \ in ^ 2[/tex]
ANswer:
Option C
QUestion 2:
For this case we have that by definition, the volume of a cylinder is given by:[tex]V = \pi * r ^ 2 * h[/tex]
Where:
r: It's the radio
h: It's the height
According to the data we have to:
[tex]r = 6.8 \ meters\\h = 14 \ meters[/tex]
Substituting in the formula:
[tex]V = \pi * (6.8) ^ 2 * 14\\V = \pi * 46.24 * 14\\V = 2032.71[/tex]
Finally, the volume of the cylinder is [tex]2032.71 \ m ^ 3[/tex]
Answer:
Option C
Question 3:
For this case we have that by definition, the volume of a cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where:
r: It's the radio
h: It's the height
According to the data we have to:
[tex]r = \frac {5} {2} = 2.5 \ feet\\h = 7.4 \ feet[/tex]
Substituting in the formula:
[tex]V = \pi * (2.5) ^ 2 * 7.4\\V = \pi * 6.25 * 7.4\\V = 145.23[/tex]
Finally, the volume of the cylinder is [tex]145.23 \ ft ^ 3[/tex]
Answer:
Option B
Question 4:
For this case we have that the volume of the bricks comes given by:
[tex]V = 11 * 5 * 3\\V = 165[/tex]
The volume of each brick is [tex]165 \ in ^ 3.[/tex]
On the other hand, we have that the volume of the crate is also obtained by multiplying its three dimensions, that is:
[tex]V = 55 * 20 * 12V = 13,200[/tex]
Thus, the volume of the crate is [tex]13,200 \ in ^ 3[/tex]
We divide the volume of the crate between the volume of the brick to know the quantity:
[tex]\frac {13,200} {165} = 80[/tex]
Thus, 80 bricks fit.
Answer:
Option A
