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If the total surface area of the right circular cylinder is 50% more than the curved surface area of that cylinder and the volume of right circular cylinder is 5488π m3, then find the curved surface of the right circular cylinder. (in m2)
- a)784π m2
- b)684π m2
- c)786π m2
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the total surface area of the right circular cylinder is 50% more t...
Given:
The total surface area of the right circular cylinder is 50% more than the curved surface area of that cylinder.
Volume of right circular cylinder = 5488π m3
Formula used:
(1.) Total surface area of cylinder = 2πr(r + h)
(2.) Curved surface area of cylinder = 2πrh
(3.) Volume of cylinder = πr2h
Where,
r = radius
h = height
Calculation:
According to the question,
⇒ 2πr(r + h) = (100% + 50%) of 2πrh
⇒ r + h = 150% of h
⇒ r + h = 3/2 of h
⇒ 2r + 2h = 3h
⇒ h = 2r
Now,
Volume of right circular cylinder = 5488π m3
⇒ πr2h = 5488π
⇒ r2(2r) = 5488
⇒ 2r3 = 5488
⇒ r3 = 2744
⇒ r = 14 m
Therefore,
⇒ h = 2r
⇒ h = 28 m
Again according to the question,
Curved surface area of cylinder = 2πrh = 784π m2
Therefore, '784π m2' is the required answer.
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Community Answer
If the total surface area of the right circular cylinder is 50% more t...
To solve this problem, we need to use the formulas for the surface area and volume of a right circular cylinder.
Let's denote the radius of the cylinder as r and the height as h.
The surface area of a right circular cylinder is given by the formula:
A = 2πrh + 2πr^2
The curved surface area of a right circular cylinder is given by the formula:
CSA = 2πrh
Given that the total surface area is 50% more than the curved surface area, we can write the equation:
A = CSA + 0.5CSA
Simplifying this equation, we get:
A = 1.5CSA
Substituting the formulas for A and CSA, we have:
2πrh + 2πr^2 = 1.5(2πrh)
Simplifying further, we get:
2πrh + 2πr^2 = 3πrh
Subtracting 2πrh from both sides, we get:
2πr^2 = πrh
Dividing both sides by πr, we get:
2r = h
Now, we can use the formula for the volume of a right circular cylinder to solve for r and h:
V = πr^2h
Given that the volume is 5488, we have:
πr^2h = 5488
Substituting 2r for h, we get:
πr^2(2r) = 5488
Simplifying further, we have:
2πr^3 = 5488
Dividing both sides by 2π, we get:
r^3 = 2744/π
Taking the cube root of both sides, we get:
r = (2744/π)^(1/3)
Substituting this value of r back into the equation 2r = h, we can find h:
h = 2r = 2(2744/π)^(1/3)
Therefore, the radius of the cylinder is (2744/π)^(1/3) and the height is 2(2744/π)^(1/3).
Let's denote the radius of the cylinder as r and the height as h.
The surface area of a right circular cylinder is given by the formula:
A = 2πrh + 2πr^2
The curved surface area of a right circular cylinder is given by the formula:
CSA = 2πrh
Given that the total surface area is 50% more than the curved surface area, we can write the equation:
A = CSA + 0.5CSA
Simplifying this equation, we get:
A = 1.5CSA
Substituting the formulas for A and CSA, we have:
2πrh + 2πr^2 = 1.5(2πrh)
Simplifying further, we get:
2πrh + 2πr^2 = 3πrh
Subtracting 2πrh from both sides, we get:
2πr^2 = πrh
Dividing both sides by πr, we get:
2r = h
Now, we can use the formula for the volume of a right circular cylinder to solve for r and h:
V = πr^2h
Given that the volume is 5488, we have:
πr^2h = 5488
Substituting 2r for h, we get:
πr^2(2r) = 5488
Simplifying further, we have:
2πr^3 = 5488
Dividing both sides by 2π, we get:
r^3 = 2744/π
Taking the cube root of both sides, we get:
r = (2744/π)^(1/3)
Substituting this value of r back into the equation 2r = h, we can find h:
h = 2r = 2(2744/π)^(1/3)
Therefore, the radius of the cylinder is (2744/π)^(1/3) and the height is 2(2744/π)^(1/3).
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