| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.97 |
| Score | 0% | 59% |
If side a = 1, side b = 3, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{73} \) | |
| \( \sqrt{5} \) | |
| \( \sqrt{162} \) | |
| \( \sqrt{10} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 12 + 32
c2 = 1 + 9
c2 = 10
c = \( \sqrt{10} \)
For this diagram, the Pythagorean theorem states that b2 = ?
c - a |
|
a2 - c2 |
|
c2 + a2 |
|
c2 - a2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
A cylinder with a radius (r) and a height (h) has a surface area of:
π r2h2 |
|
2(π r2) + 2π rh |
|
π r2h |
|
4π r2 |
A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r2h and the surface area is 2(π r2) + 2π rh.
If a = 1, b = 4, c = 6, and d = 4, what is the perimeter of this quadrilateral?
| 15 | |
| 20 | |
| 22 | |
| 16 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 1 + 4 + 6 + 4
p = 15
The dimensions of this cylinder are height (h) = 4 and radius (r) = 8. What is the surface area?
| 12π | |
| 90π | |
| 192π | |
| 110π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(82) + 2π(8 x 4)
sa = 2π(64) + 2π(32)
sa = (2 x 64)π + (2 x 32)π
sa = 128π + 64π
sa = 192π