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thomaskilajuwon
08.07.2021 •
Mathematics
A square pyramid is inscribed in a rectangular prism. A cone is inscribed in a cylinder. The pyramid and the cone have the same volume. Part of the volume of the rectangular prism, 1 V 1 , is not taken up by the square pyramid. Part of the volume of the cylinder, 2 V 2 , is not taken up by the cone. What is the relationship of these two volumes, 1 V 1 and 2 V 2 ?
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Ответ:
V₂ = V₁
Step-by-step explanation:
Let the height of the rectangular prism = h
Let s represent the side length of the base of the square prism, we have;
The volume of the prism,
= s²·h
The volume of the square pyramid,
= (1/3)·s²·h
∴ V₁ = The area not taken up by the square pyramid =
- ![V_{pyramid}](/tpl/images/1390/9873/83531.png)
∴ V₁ = s²·h - (1/3)·s²·h = (2/3)·s²·h
Similarly, for the cylinder, we have;
Let h represent the height of the cylinder
Let r represent the radius of the base of the cone, we have;
Therefore;
The volume of the cylinder,
= π·r²·h
The volume of the cone,
= (1/3)·π·r²·h
∴ V₂ = π·r²·h - (1/3)·π·r²·h = (2/3)·π·r²·h
V₂ = (2/3)·π·r²·h
Therefore;
(1/3)·π·r²·h = (1/3)·s²·h
∴ π·r² = s²
Therefore, V₂ = (2/3)·π·r²·h = V₂ = (2/3)·s²·h = V₁
V₂ = V₁.
Ответ:
Graph the inequality by finding the boundary line, then shading the appropriate area.
y
≤
3
x
−
2
Step-by-step explanation: