9514 1404 393
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.
__
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.
