Sum of the radius of the base and height of a cylinder is 21 cm and the curved surface area of the cylinder is 616 sq. cm, find the total surface area of the cylinder. PLEASE HELP ME AS FAST AS POSSIBLE With a full process.

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