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If the numerical value of the volume of a right circular cylinder and its curved surface area are equal, then its radius is.
- a)2 units
- b)4 units
- c)3 units
- d)6 units
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the numerical value of the volume of a right circular cylinder and...
Explanation:
To solve this problem, let's first determine the formulas for the volume and curved surface area of a right circular cylinder.
The volume of a right circular cylinder can be calculated using the formula: V = πr^2h, where r is the radius and h is the height of the cylinder.
The curved surface area of a right circular cylinder can be calculated using the formula: CSA = 2πrh, where r is the radius and h is the height of the cylinder.
Now, let's assume the radius of the cylinder is 'r' units.
Step 1: Calculate the volume:
Given that the volume of the cylinder is equal to its curved surface area, we can equate the formulas:
πr^2h = 2πrh
Step 2: Simplify the equation:
Divide both sides of the equation by πr:
r^2h = 2rh
Step 3: Cancel out the common term:
Divide both sides of the equation by r:
rh = 2h
Step 4: Simplify the equation:
Divide both sides of the equation by h:
r = 2
Therefore, the radius of the right circular cylinder is 2 units.
Conclusion:
The correct answer is option 'A' (2 units) as the numerical value of the volume of a right circular cylinder and its curved surface area are equal when the radius is 2 units.
To solve this problem, let's first determine the formulas for the volume and curved surface area of a right circular cylinder.
The volume of a right circular cylinder can be calculated using the formula: V = πr^2h, where r is the radius and h is the height of the cylinder.
The curved surface area of a right circular cylinder can be calculated using the formula: CSA = 2πrh, where r is the radius and h is the height of the cylinder.
Now, let's assume the radius of the cylinder is 'r' units.
Step 1: Calculate the volume:
Given that the volume of the cylinder is equal to its curved surface area, we can equate the formulas:
πr^2h = 2πrh
Step 2: Simplify the equation:
Divide both sides of the equation by πr:
r^2h = 2rh
Step 3: Cancel out the common term:
Divide both sides of the equation by r:
rh = 2h
Step 4: Simplify the equation:
Divide both sides of the equation by h:
r = 2
Therefore, the radius of the right circular cylinder is 2 units.
Conclusion:
The correct answer is option 'A' (2 units) as the numerical value of the volume of a right circular cylinder and its curved surface area are equal when the radius is 2 units.
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Community Answer
If the numerical value of the volume of a right circular cylinder and...
Volume of right circular cylinder = Curved surface area of cylinder
pπ2h = 2πrh [where, r - radius; h - height]
⇒ r = 2 units
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If the numerical value of the volume of a right circular cylinder and its curved surface area are equal, then its radius is.a)2 unitsb)4 unitsc)3 unitsd)6 unitsCorrect answer is option 'A'. Can you explain this answer?
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