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4vir4ik [10]
3 years ago
13

A right square pyramid with base edges of length $8\sqrt{2}$ units each and slant edges of length 10 units each is cut by a plan

e that is parallel to its base and 3 units above its base. What is the volume, in cubic units, of the new pyramid that is cut off by this plane?

Mathematics
1 answer:
seropon [69]3 years ago
5 0

Answer:

32 unit^{3}

Step-by-step explanation:

Given:

  • The slant length 10 units
  • A right square pyramid with base edges of length 8\sqrt{2}

Now we use  Pythagoras to get the slant height in the middle of each triangle:

\sqrt{10^{2 - (4\sqrt{2} ^{2} }) } = \sqrt{100 - 32} = \sqrt{68}  units

One again, you can use Pythagoras again to get the perpendicular height of the entire pyramid.

\sqrt{68-(4\sqrt{2} ^{2} )} = \sqrt{68 - 32} = 6 units.

Because slant edges of length 10 units each is cut by a plane that is parallel to its base and 3 units above its base. So we have the other dementions of the small right square pyramid:

  • The height 3 units
  • A right square pyramid with base edges of length 4\sqrt{2}

So the volume of it is:

V  = 1/3 *3* 4\sqrt{2}

= 32 unit^{3}

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76 div 4<br><br> a)15<br><br> b) 8<br><br> c) 19<br><br> d) 0<br><br> Explain
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Answer:

C. 19.  

Step-by-step explanation:

Let's find the answer.

Step 1:  divide the first number of 76, which is 7, by 4 and find the integer part.

7/4=1.75, so the integer part is 1.

Step 2: subtract from 7 the (integer part times 4)

7-(1*4)=3

Step 3: put toether the result (3) and the second number of 76, which is 6, so the result is 36.

Step 4: find how many times we need to add 4s to reach 36, so:

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Step 5: put together the two resulted numbers calculated in step 1, which is 1, and step 4, which is 9:

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