Answer:
5.1
Step-by-step explanation:
Since there is no diagram provided here, we assume that c is the length of the hypotenuse, so we have ...
c² = a² +b² . . . . . . Pythagorean theorem
c² = 2.7² +4.3² = 25.78
c = √25.78 ≈ 5.0774
c ≈ 5.1
Answer:
Tyler didn't make a mistake
Step-by-step explanation:
3(x+4)=-18
(x+4)=-18/3 (divide by 3 on both the sides)
x+4=-6
x=-6-4 (subtract 4 from both the sides)
x=-10
Answer:
Very last choice is the answer.
Step-by-step explanation:
Remark
The thing that is most important is that the horizontal line connect h and the radius is parallel to the cut of the sphere if it was placed right in the middle. That line swings around as though the center was a pivot.
Solution
- So what you have is a circle when that line goes around that part of the sphere.
- To find the length of that line, use the Pythagorean Theorem. Call the line r1.
- r1 ^2 = r^2 - h^2
- So the area is pi * r1^2
- Area = pi (r^2 - h^2)
- The very last one is the answer.
The volume of the cake is 1470 in³.
volume of a cylinder = πr² x height
(Think about how a cylinder is basically a bunch of circles stacked on top of each other. To find the volume, first you need the area of the circle (πr², then you multiply by how many circles you are stacking on top of each other (height))
we know the diameter of the cylinder is 12 in. and the radius is half of the diameter.
half of 12 is 6, therefore the radius is 6 in. or r = 6
Assuming pi is 3.14, solve for the height of the cylinder
1470 = (3.14)(6²)(height)
1470 = 3.14 x 36 x height
1470 = 113.04 x height
height ≈ 13 in
Now that we know the height of the cylinder is about 13 in., we know the height of the cone, because the problem says that the height of the cone is half the height of the cylinder.
half of 13 is 6.5, therefore the height of the cone is 6.5
the radius of the cone is the same as that of the cylinder, 6 in.
volume of a cone = πr² × (height ÷ 3)
volume of the cone = (3.14)(6²)(6.5 ÷ 3)
volume of the cone = (3.14)(36)(2.16666)
volume of the cone = 244.92 in³
Now all that's left to find the volume of the whole cake is to add the volume of the cylinder to the volume of the cone.
1470 + 244.92 = 1714.92 in³
Answer:m+3
Step-by-step explanation:
