Question

The volume of a cylinder is 12,566.4 cm3. The height of the cylinder is 8 cm.

Answer 1

Using the formulas here: http://www.1728.org/diamform.htm

A)  Volume   =   π • r² • height
radius^2 = Volume / (PI*height)
radius^2 = 12,566.4 / (PI * 8)
radius^2 =  500.0011692175
radius = 22.3607059195
radius (rounded) = 22.4 cm

B) Area of base = PI * radius^2
Area of base = 3.14159265 * 500
Area of base = 1,570.7963267949
Area of base (rounded) = 1,570.8 square cm
 
C) lateral area = 2 • π • r • height
lateral area = 2 • π • 22.4 * 8
lateral area = 1,125.9468070466
lateral area = 1,125.9 square cm

D) Total Surface Area = (2 • π • r²) + (2 • π • r • height)
Total Surface Area = 2 * (top AND bottom area which is the Part B answer times 2) + (the lateral area which is the Part C answer)

Total Surface Area = ( 2 * 1,570.8 ) + (1,125.9)
Total Surface Area = 3,141.6 + 1,125.9
Total Surface Area = 4,267.5 square cm