Which of the following equations could be used to solve the problem? A. x + (11 - x) = 1.70. B. 25x + 10(11 - x) = 1.70. C. 0.10x + 0.25(11 - x) = 1.70.

925.04cm²

Step-by-step explanation:

Curved surface area of a cylinder = 2πrh

r is the radius

h is the height

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

Recall:

CSA =  2πrh

616 = 2πrh 2

Substitute equation 1 into 2;

616 = 2π(21-h)h

616 = 2π(21h-h²)

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

Since r = 21-h

r = 21 - 13.985

Using r = 7.015

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