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There is a right circular cylinder which has a base diameter of 16 units and a height of 6π units. An ant is at the circumference of the base of the cylinder and wants to reach the sugar cube which is placed at top-most point of diametrically opposite end from the ant. What is the minimum possible distance that ant has to travel?
- a)10√2π
- b)10π
- c)6√2π
- d)8√2π
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
There is a right circular cylinder which has a base diameter of 16 uni...
It is given that the base has a diameter of 16 units, it implies that the radius is 8 units and hence the circumference is 16π units
If we cut open the cylinder into a 2-D paper then, the ant has to travel a horizontal distance of half the circumference = 8π units. and vertical distance will be 6π.
In order to minimise the distance, he has to travel along the hypotenuse formed which is of length =
If we cut open the cylinder into a 2-D paper then, the ant has to travel a horizontal distance of half the circumference = 8π units. and vertical distance will be 6π.
In order to minimise the distance, he has to travel along the hypotenuse formed which is of length =
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
There is a right circular cylinder which has a base diameter of 16 uni...
To find the volume and surface area of the right circular cylinder, we can use the following formulas:
Volume of a cylinder: V = πr^2h
Surface area of a cylinder: A = 2πr^2 + 2πrh
Given:
Base diameter = 16 units
Height = 6 units
The base diameter is twice the radius (since diameter = 2 * radius), so the radius of the cylinder is 16/2 = 8 units.
Using the formulas, we can calculate the volume and surface area:
Volume:
V = π(8^2)(6)
V = π(64)(6)
V = 384π cubic units
Surface area:
A = 2π(8^2) + 2π(8)(6)
A = 2π(64) + 2π(48)
A = 128π + 96π
A = 224π square units
Therefore, the volume of the cylinder is 384π cubic units and the surface area is 224π square units.
Volume of a cylinder: V = πr^2h
Surface area of a cylinder: A = 2πr^2 + 2πrh
Given:
Base diameter = 16 units
Height = 6 units
The base diameter is twice the radius (since diameter = 2 * radius), so the radius of the cylinder is 16/2 = 8 units.
Using the formulas, we can calculate the volume and surface area:
Volume:
V = π(8^2)(6)
V = π(64)(6)
V = 384π cubic units
Surface area:
A = 2π(8^2) + 2π(8)(6)
A = 2π(64) + 2π(48)
A = 128π + 96π
A = 224π square units
Therefore, the volume of the cylinder is 384π cubic units and the surface area is 224π square units.
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There is a right circular cylinder which has a base diameter of 16 units and a height of 6π units. An ant is at the circumference of the base of the cylinder and wants to reach the sugar cube which is placed at top-most point of diametrically opposite end from the ant. What is the minimum possible distance that ant has to travel?a)10√2πb)10πc)6√2πd)8√2πCorrect answer is option 'B'. Can you explain this answer?
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