The radius of the base and the height of a closed cylinder are 14 cm and 14 cm, respectively. The total surface area of the cylinder is equal to the area of a circle. What will be the diameter of the circle? [Use pi = 22/7 ]
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 56 cm
The total surface area of a cylinder is given by:
2πr(r + h)
where r is the radius of the base, h is the height of the cylinder, and π is the constant pi.
In this problem, we have r = 14 cm and h = 14 cm. Therefore, the total surface area of the cylinder is:
2π(14) (14 + 14) = 2π(14) (28) = 784π sq.cm
The area of a circle is given by:
πr2
where r is the radius of the circle.
πr2 = 784π
r2= 784
r = √784 = 28
The diameter of the circle is twice the radius, so:
d = 2r = 2(28) = 56 cm
Therefore, the diameter of the circle is 56 cm.