Question

1. a cubic container has edges of 2 ft. what is its volume in cubic feet?

section 3: angles, slope, and practical problems (5 questions)

1. a ramp rises 2 feet over a run of 12 feet. what is the slope as a ratio?
2. a miter cut needs to be made at 45 degrees. what is the complementary angle?
3. youre framing a wall with studs spaced every 16 inches. how many studs are needed for a 12 - foot wall?
4. if a bundle of shingles covers 33.3 square feet, how many bundles are needed to cover a 1,000 sq ft roof?
5. a window is 30 inches wide. you want to center it on a 96 - inch wide wall. how far from each edge should it be placed?

Explanation:

Step1: Recall volume formula for cube

The volume $V$ of a cube is given by $V = s^3$, where $s$ is the length of an edge.

Step2: Substitute the value of the edge length

Here, $s = 2$ ft. So, $V=2^3$.

Step3: Calculate the result

$2^3=2\times2\times2 = 8$ cubic feet.

Step1: Recall slope formula

The slope $m$ of a line is given by the ratio of the rise to the run, $m=\frac{\text{rise}}{\text{run}}$.

Step2: Substitute rise and run values

The rise is 2 feet and the run is 12 feet. So, $m = \frac{2}{12}=\frac{1}{6}$.

Step1: Recall complementary - angle definition

Two angles are complementary if their sum is 90 degrees. Let the given angle be $\theta = 45$ degrees. Let the complementary angle be $\alpha$. Then $\theta+\alpha = 90^{\circ}$.

Step2: Solve for the complementary angle

$\alpha=90 - 45=45$ degrees.

Step1: Convert wall length to inches

Since 1 foot = 12 inches, a 12 - foot wall has a length of $12\times12 = 144$ inches.

Step2: Calculate number of intervals

The number of 16 - inch intervals in a 144 - inch wall is $\frac{144}{16}=9$.

Step3: Calculate number of studs

The number of studs is one more than the number of intervals, so the number of studs is $9 + 1=10$.

Answer:

8