A 3-inch by 5-inch index card is rotated around a horizontal line and a vertical line to produce two different solids. Which sol
1 answer:
This question is incomplete, the missing diagram is uploaded along this answer below;
Answer:
horizontal V₁ ( 141.37 in³ ) is less than vertical V₂ ( 235.62 in³ )
Step-by-step explanation:
Given the data in the question and as illustrated in the image below;
from the image,
We find the volume of the solid obtained by rotating the card around a horizontal line;
Volume of the cylinder V₁ = πr²h
given that; radii = 3 in and height = 5 in
we substitute
V₁ = π × (3)² × 5
V₁ = π × 9 × 5
V₁ = 141.37 in³
Next we find the volume of the solid obtained by rotating the card around a vertical line;
Volume of the cylinder V₂ = πr²h
given that; radii = 5 in and height = 3 in
we substitute
V₂ = π × (5)² × 3
V₂ = π × 25 × 3
V₂ = 235.62 in³
Hence horizontal V₁ ( 141.37 in³ ) is less than vertical V₂ ( 235.62 in³ )
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