Answer:
The remaining interior angles of this triangle are 140º and 10º
Step-by-step explanation:
The sum of the interior angles of a triangle is always 180º.
A triangle has 3 angles. In this problem, we have one of them, that i am going to call A1 = 30º.
The sum of a interior angle with it's respective exterior angle is also always 180º.
We have that one of the exterior angles is equal to 40°. So it's respective interior angle is
40º + A2 = 180º
A2 = 180º - 40º
A2 = 140º
Now we have two interior angles, and we know that the sum of the 3 interior angles is 180º. So:
A1 + A2 + A3 = 180º
A3 = 180º - A1 - A2
A3 = 180º - 30º - 140º
A3 = 180º - 170º
A3 = 10º
Let the width be x, then length = 4x - 7
Perimeter = 2(length + width)
2(x + 4x - 7) = 46
2(5x - 7) = 46
10x - 14 = 46
10x = 60
x = 6
Therefore, width is 6 and length is 4(6) - 7 = 24 - 7 = 17
What is asked in the problem is simply the volume of the solid rubber ball. The volume of sphere given the diameter may be calculated by,
V = πd^3 / 6
Substituting the given value of diameter,
V = (π x 3³) / 6 = 9π/2 or 14.14
Thus, one needs approximately 14.14 in³ of material.
