Answer:
925.04cm²
Step-by-step explanation:
Curved surface area of a cylinder = 2πrh
If the sum of the radius of the base and height of the cylinder is 21 cm, then;
r + h = 21
r = 21-h..... 1
The curved surface area is expressed according to the formula
CSA = 2πrh
Substitute the value of CSA given into the formula
616 = 2πrh ....2
Substitute equation 1 into 2;
]616 = 2π(21-h)h
616 = 2π(21h-h²)
Note that π = 3.14
616 = 42(3.14)h - 2(3.14)h²
616 = 131.88h - 6.28h²
98.09 = 21h - h²
h²-21h+98.09 = 0
h = 21±√21²-4(98.09)/2
h = 21±√441-392.36/2
h = 21±√48.64/2
h = 21±6/97/2
h = 21+6.97/2 and 21-6.97/2
h = 27.97/2 and 14.03/2
h = 13.985 and 7.015
Recall that r = 21-h
r = 21 - 13.985
Substitute r = 7.015 into the total surface area of the cylinder
The total surface area = 2πrh + 2πr²
The total surface area = 616 + 2(3.14)7.015²
The total surface area = 616 + 309.04
The total surface area = 925.04
Hence the total surface area of the cylinder is 925.04cm²