SOLUTION: A cylinder of radius length 8 cm has curved surface area = 320cm2. A rectangular block of height 13 cm, width 16 cm and length cm has the same volume as the cylinder. Calculate

Algebra ->  Surface-area -> SOLUTION: A cylinder of radius length 8 cm has curved surface area = 320cm2. A rectangular block of height 13 cm, width 16 cm and length cm has the same volume as the cylinder. Calculate       Log On


   

Question 1004309: A cylinder of radius length 8 cm has curved surface area = 320cm2. A rectangular block of height 13 cm, width 16 cm and length cm has the same volume as the cylinder.
Calculate the length of the block correct to the nearest whole number.
Hint: Find height of cylinder
Length = ? cm
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Cylinder:
Circumference%2Ah=320
Using h for its length or "height".
2%2Api%2A8%2Ah=320
h=320%2F%282%2A8%2Api%29
h=20%2Fpi
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The volume of this cylinder is h%2Api%2Ar%5E2 and now h is known.


Rectangle:
Let the unknown length be x.
Volume is described to be equal to that of the cylinder.
13%2A16%2Ax=h%2Api%2Ar%5E2
13%2A16%2Ax=%2820%2Fpi%29pi%2A8%5E2
13%2A16%2Ax=20%2A8%5E2
x=%2820%2A8%5E2%29%2F%2813%2A16%29
x=%2820%2A64%29%2F%2813%2A16%29
x=20%2A4%2F13
x=80%2F13
or
highlight%28x=6%262%2F13%29, centimeters