| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
The dimensions of this cylinder are height (h) = 1 and radius (r) = 3. What is the volume?
| 32π | |
| 64π | |
| 25π | |
| 9π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(32 x 1)
v = 9π
Which types of triangles will always have at least two sides of equal length?
equilateral and right |
|
equilateral and isosceles |
|
equilateral, isosceles and right |
|
isosceles and right |
An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.
If the area of this square is 64, what is the length of one of the diagonals?
| 2\( \sqrt{2} \) | |
| 9\( \sqrt{2} \) | |
| 8\( \sqrt{2} \) | |
| 7\( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{64} \) = 8
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 = 82 + 82
c2 = 128
c = \( \sqrt{128} \) = \( \sqrt{64 x 2} \) = \( \sqrt{64} \) \( \sqrt{2} \)
c = 8\( \sqrt{2} \)
What is the area of a circle with a diameter of 8?
| 25π | |
| 49π | |
| 16π | |
| 81π |
The formula for area is πr2. Radius is circle \( \frac{diameter}{2} \):
r = \( \frac{d}{2} \)
r = \( \frac{8}{2} \)
r = 4
a = πr2
a = π(42)
a = 16π
If side a = 9, side b = 7, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{85} \) | |
| \( \sqrt{10} \) | |
| \( \sqrt{130} \) | |
| \( \sqrt{74} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 92 + 72
c2 = 81 + 49
c2 = 130
c = \( \sqrt{130} \)