The volume of a cylinder is 12,566.4 cm3. the height of the cylinder is 8 cm. a) find the radius of the cylinder to the nearest tenth of a centimeter. b) find the area of the base of the cylinder to the nearest tenth of a centimeter. c) find the lateral area to the nearest tenth of a centimeter. d) find the surface area of the cylinder. i know that the radius is 24 but what's b, c,d?

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

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

ac ≅ ab (given)< cax ≅ < bax   (given)ax ≅ ax (common side)

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

ac ≅ ab (given)< cay ≅ < bay (since < cax ≅ < bax is given and xy is the extension of line ax)ay ≅ ay (common side)

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)