Answer:
The volume of the resulting cylinder is 385 cm³
Step-by-step explanation:
The formula of the rule of a cylinder is V = π r² h, where
- r is the radius of its base
When a rectangular paper folded to form a cylinder, then one of its dimension will be the circumference of the base and the other dimension will be the height of the resulted cylinder
∵ ABCD is a rectangle
∵ It is folded where AB coincides with DC
∴ AB is the height of the resulted cylinder
∴ BC is the circumference of the base of the resulted cylinder
∵ AB = 10 cm
∴ h = 10 cm
∵ BC = 22 cm
∴ The circumfrence of the base = 22 cm
∵ The circumference of a circle = 2 π r
→ Equate the rule by 22 to find r
∴ 2 π r = 22
∵ π = [tex]\frac{22}{7}[/tex]
∴ 2 × [tex]\frac{22}{7}[/tex] × r = 22
∴ [tex]\frac{44}{7}[/tex] r = 22
→ Divide both sides by [tex]\frac{44}{7}[/tex]
∴ r = 3.5 cm
→ Use the formula of the volume above to find the volume of the cylinder
∵ V = [tex]\frac{22}{7}[/tex] × (3.5)² × (10)
∴ V = 385 cm³
∴ The volume of the resulted cylinder is 385 cm³
