A piece of paper has a
1 answer:
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
- h is the height of it
<em>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</em>
∵ 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 =
∴ 2 × × r = 22
∴ r = 22
→ Divide both sides by
∴ r = 3.5 cm
→ Use the formula of the volume above to find the volume of the cylinder
∵ V = × (3.5)² × (10)
∴ V = 385 cm³
∴ The volume of the resulted cylinder is 385 cm³
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Answer: (b) exactly one plane contains a given line and a point not on the line.
Step-by-step explanation: The basic postulates of geometry are very-well known to all of us. For example-
(i) The intersection of two lines determines a point,
(ii) Two parallel lines give result to a plane,
(iii) A line and a point not on the line determines a plane, etc...
Thus, with the help of the third point, we can easily arrive at the conclusion that a given line and a point not lying on the line is contained in a plane. For example- see the attached figure, AB is a line and P is any point not on the line. They both contained in the plane ABC.
Hence, the correct option is (b).
