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 π = $\frac{22}{7}$]
Answer & explanation
Correct answer: option 1
We know that,
The total surface area of the cylinder = 2πr(r + h )
The area of a circle = πR2
We have,
radius = 14 cm
height = 14 cm
As per the question,
The total surface area of the cylinder = The area of a circle
2πr(r + h ) = πR2
2r(r + h ) = R2
2 × 14 (14 + 14 ) = R2
R2 = 282
R = 28 cm
Diameter of the circle = 2 × 28 = 56 cm