Question 203267
FInd the lateral surface area, the total surface area, and the volume of a cylinder whose radius (r) is 3 cm. and whose height (h) is 10 cm.
a) Lateral surface area is:
{{{A[l] = 2(pi)r*h}}} (Area = Circumference times the height) Substitute r = 3 and h = 10.
{{{A[l] = 2(pi)(3)(10)}}}
{{{highlight(A[l] = 60(pi))}}} This is the exact answer.  For an approximation, substitute {{{pi = 3.14}}} to get:
{{{A[l] = 60(3.14)}}}
{{{highlight_green(A[l] = 188.4)}}}sq.cm.
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b) The total surface area of the cylinder is the sum of the lateral surface area (see a) above) and the areas of the top & bottom of the cylinder.
These areas (top & bottom) are the same so you need compute only one and then double it to get both.
Area of the top:
{{{A[t] = (pi)r^2}}} Substitute r = 3.
{{{A[t] = (pi)(3)^2}}}
{{{A[t] = 9(pi)}}} now double this to include the bottom:
{{{A[b] = 2(9)(pi)}}}
{{{highlight(A[b] = 18(pi))}}} For an approximation, substitute {{{pi = 3.14}}}
{{{A[b] = (18)(3.14)}}}
{{{highlight_green(A[b] = 56.52)}}}sq.cm.
Now add this to the lateral surface area ({{{60(pi)}}}) to get:
{{{A[T] = 60(pi)+18(pi)}}}
{{{highlight(A[T] = 78(pi))}}} Exact answer, or approximately:
{{{highlight_green(A[T] = 244.92)}}}sq.cm.
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c) The volume of a cylinder is given by:
{{{V = (pi)*r^2*h}}} Substitute r = 3 and h = 10.
{{{V = (pi)(3)^2(10)}}}
{{{highlight(V = 90(pi))}}} or approximately:
{{{V = 90(3.14)}}}
{{{highlight_green(V = 282.6)}}}cu.cm.