Philip P. answered • 05/15/14

Effective and Patient Math Tutor

Tutor

Volume = (Area of the base)(Height) = (pi)*r

^{2}*hWhere pi=3.14159, r = the cylinder's radius, and h = its height. So, for your problem:

(pi*r

^{2}*h) = 6433.98175r

^{2}*h = (6433.98175)/(pi) [Divided both sides by pi]r

^{2}*h = 2048h = 2048/r

^{2}Pick a value of r, then use the above equation to determine the value of h that will give a volume of 6433.98175 cm

^{3}. For example, for r = 10 cmh = 2048/10

^{2}= 2048/100 = 20.48 cmSo the combination is

**r = 10 cm, h = 20.48 cm**. Check:Volume = (pi)*(10

^{2})(20.48) = (3.14159)(100)(20.48) = 6433.98175The formula for the cylinder's surface area is:

Surface Area = 2(pi)r

^{2}+ 2(pi)rh = 2(pi)r(r+h)Use this formula to compute the surface areas for your selected values of r and h. For the combination r=10, h=20.48

Surface Area = 2(3.14159)(10)(10+20.48) = 1915.11 cm

^{2}
Andre Y.

05/15/14