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Tcecarenko [31]
3 years ago
6

A rectangular prism has a height of 12 cm and a square base with sides measuring 5 cm. A pyramid with the same base and the heig

ht of the prism is placed inside the prism. What is the volume of the space outside the pyramid but inside the prism?
Mathematics
1 answer:
Ksju [112]3 years ago
3 0
The answer is 200 cm³


The volume of the rectangular prism (V1) is:
V1 = l · w · h                       (l - length,  w - width,  h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
Thus: V1 = 12 · 5 · 5 = 300 cm³

The volume of pyramid (V2) is:
V2 = 1/3 · l · w · h                   (l - length,  w - width,  h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
V2 = 1/3 · 12 · 5 · 5 = 1/3 · 300 = 100 cm³


The volume of the space outside the pyramid but inside the prism (V) is a difference between the volume of the rectangular prism (V1) and the volume of the pyramid (V2): 
V = V1 - V2 = 300 cm³ - 100 cm³ = 200 cm³
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5 0
3 years ago
Help me Please....................
MakcuM [25]

9514 1404 393

Answer:

  1.3363

Step-by-step explanation:

The basic idea here is to find an expression for the direction vector between a point on L1 and a point on L2. Then, solve for the points on L1 and L2 that make that vector perpendicular to both lines L1 and L2. (The dot product of direction vectors is zero.) The distance between the points found is the shortest distance between the lines.

__

Let P be a point on L1. Then the parametric equation for P is ...

  P = (6t, 0, -t) . . . . . . origin + t × direction vector

Let Q be a point on L2. The direction vector for L2 is given by the difference between the given points. It is (4-1, 1-(-1), 6-1) = (3, 2, 5). Then the parametric equation for Q is ...

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The direction vector for PQ is ...

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The solution to these equations is ...

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Then (Q-P) becomes (94, -1551, 564)/1237, and its length is ...

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