Question

deep. Calculate its volume (in cm in terms of m). [JAMB] 500 A right pyramid on a base 10 m square is 15 m high. a Find the volume of the pyramid. b If the top 6 m of the pyramid are removed, what is the volume of the remaining frustum?​

Answer 1

Answer:

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Step-by-step explanation:

that is the procedure above

Answer 2

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Answer:

  a. 500 m³

  b. 468 m³

Step-by-step explanation:

Given:

  a square base pyramid with side 10 m and height 15 m

Find:

  a) the volume of the pyramid

  b) the volume of the remaining frustum with the top 6 m removed

Solution:

a) The volume of the pyramid is given by the formula ...

  V = 1/3Bh

where B = s², the area of the square base, and h is the height

  V = (1/3)(10 m)²(15 m) = 500 m³

The volume of the pyramid is 500 m³.

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b) The top 6 meters constitute a similar pyramid with a scale factor of 6/15 = 2/5. The volume of that portion is then the total volume multiplied by the cube of the scale factor:

  volume of top 6 feet = (500 m³)(2/5)³ = 32 m³

Then the volume of the remaining frustum is ...

  500 m³ -32 m³ = 468 m³

The volume of the remaining frustum is 468 m³.