1. The problem involves comparing the volumes of two cylinders made from the same rectangular sheet of paper, one rolled along its length and the other along its width.
2. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height.
3. When the paper is rolled along its length (11 inches), the circumference of the base is 11 inches, so the radius is 11/(2π) inches, and the height is 8.5 inches.
4. When the paper is rolled along its width (8.5 inches), the circumference of the base is 8.5 inches, so the radius is 8.5/(2π) inches, and the height is 11 inches.
5. Calculating both volumes:
- Volume when rolled along length: V₁ = π × (11/(2π))² × 8.5 ≈ 81.8 in³
- Volume when rolled along width: V₂ = π × (8.5/(2π))² × 11 ≈ 63.2 in³
6. Comparing the volumes shows that V₁ > V₂, meaning the cylinder rolled along the longer side has a larger volume.
7. Therefore, Haley’s hypothesis that the cylinder with the greater circumference (rolled along the longer side) would have a larger volume is correct.
Parent Tip: Review the logic above to help your child master the concept of grade 6 reading comprehension worksheet pdf.
