| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.08 |
| Score | 0% | 62% |
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
h x l x w |
|
h2 x l2 x w2 |
|
2lw x 2wh + 2lh |
|
lw x wh + lh |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.
For this diagram, the Pythagorean theorem states that b2 = ?
c2 - a2 |
|
a2 - c2 |
|
c - a |
|
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, \(c = \sqrt{a + b}\)
Simplify 8a x 2b.
| 16\( \frac{a}{b} \) | |
| 16a2b2 | |
| 16ab | |
| 16\( \frac{b}{a} \) |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
8a x 2b = (8 x 2) (a x b) = 16ab
Solve for z:
-z + 4 = -8 - 2z
| -\(\frac{4}{9}\) | |
| -12 | |
| -8 | |
| \(\frac{1}{2}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
-z + 4 = -8 - 2z
-z = -8 - 2z - 4
-z + 2z = -8 - 4
z = -12
The dimensions of this cylinder are height (h) = 3 and radius (r) = 4. What is the surface area?
| 144π | |
| 216π | |
| 36π | |
| 56π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(42) + 2π(4 x 3)
sa = 2π(16) + 2π(12)
sa = (2 x 16)π + (2 x 12)π
sa = 32π + 24π
sa = 56π