Question

A 3-inch by 5-inch index card is rotated around a horizontal line and a vertical line to produce two different solids. Which solid has a greater volume

Answer 1

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 )