| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.66 |
| Score | 0% | 73% |
The dimensions of this cube are height (h) = 6, length (l) = 8, and width (w) = 4. What is the volume?
| 288 | |
| 360 | |
| 32 | |
| 192 |
The volume of a cube is height x length x width:
v = h x l x w
v = 6 x 8 x 4
v = 192
What is the circumference of a circle with a radius of 7?
| 8π | |
| 14π | |
| 10π | |
| 36π |
The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:
c = πd
c = π(2 * r)
c = π(2 * 7)
c = 14π
If the area of this square is 49, what is the length of one of the diagonals?
| 3\( \sqrt{2} \) | |
| 4\( \sqrt{2} \) | |
| 7\( \sqrt{2} \) | |
| 5\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{49} \) = 7
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 72 + 72
c2 = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)
The dimensions of this cylinder are height (h) = 8 and radius (r) = 1. What is the volume?
| 75π | |
| 175π | |
| 8π | |
| 50π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(12 x 8)
v = 8π
What is 2a + 6a?
| 8a2 | |
| -4a2 | |
| 12a | |
| 8a |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
2a + 6a = 8a