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Paha777 [63]
3 years ago
6

A rectangular prism has a length of 8 in., a width of 4 in., and a height of 214 in.

Mathematics
1 answer:
Ivan3 years ago
8 0

For this case we have that by definition, the volume of a rectangular prism is given by:

V = A_ {b} * h

Where:

A_ {b}: It is the area of the base

h: It is the height

So:

A_ {b} = 8 * 4 = 32 \ in ^ 2\\h = 214 \ in

The volume of the prism is:

V = 32 * 214 = 6848 \ in ^ 3

Now, the volume of the cubes is:

V = (14) ^ 3 = 2744 \ in ^ 3

Thus, we divide and find the number of cubes to fill the prism:

n = \frac {6848 \ in ^ 3} {2744 \ in ^ 3}\\n = 2.5

ANswer:

n = 2.5

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Answer:

  (d)  m∠AEB = m∠ADB

Step-by-step explanation:

The question is asking you to compare the measures of two inscribed angles. Each of the inscribed angles intercepts the circle at points A and B, which are the endpoints of a diameter.

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<h3>applicable relations</h3>

Several relations are involved here.

  • The measures of the arcs of a circle total 360°
  • A diameter cuts a circle into two congruent semicircles
  • The measure of an inscribed angle is half the measure of the arc it intercepts
<h3>application</h3>

In the attached diagram, we have shown inscribed angle ADB in blue. The semicircular arc it intercepts is also shown in blue. A semicircle is half a circle, so its arc measure is half of 360°. Arc AEB is 180°. That means inscribed angle ADB measures half of 180°, or 90°. (It is shown as a right angle on the diagram.)

If Brenda draws angle AEB, it would look like the angle shown in red on the diagram. It intercepts semicircular arc ADB, which has a measure of 180°. So, angle AEB will be half that, or 180°/2 = 90°.

The question is asking you to recognize that ∠ADB = 90° and ∠AEB = 90° have the same measure.

  m∠AEB = m∠ADB

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<em>Additional comment</em>

Every angle inscribed in a semicircle is a right angle. The center of the semicircle is the midpoint of the hypotenuse of the right triangle. This fact turns out to be useful in many ways.

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