This shape is a little weird. Before we calculate anything, we should come up with an overall surface area formula. The total surface area is the lateral area of a cylinder, and the two lateral areas of the cones. *SA* = *L*_{Cylinder} + 2*L*_{Cone}
The lateral area of a cylinder is the circumference of the circle times the length of the cylinder. Circumference is two times the radius times our favorite dessert. *L*_{Cylinder} = 2π*rh*
*L*_{Cylinder} = 2π(0.5 ft)(4 ft)
*L*_{Cylinder} = 12.57 ft^{2}
The lateral area of the cone has its own formula too. *L*_{Cone} = π*rl*
We don't know the slant height yet, but we can figure it out. Pythagoras knows what's up. *a*^{2} + *b*^{2} = *c*^{2} (0.5 ft)^{2} + (2 ft)^{2} = c^{2}
*c* = *l* ≈ 2.06 ft
Now we're ready to calculate the lateral area of the cone. *L*_{Cone} = π*rl*
*L*_{Cone} = π(0.5 ft)(2.06 ft)
*L*_{Cone} = 3.24 ft^{2}
One final step remains. *SA* = *L*_{Cylinder} + 2*L*_{Cone}
*SA* = (12.57 ft^{2}) + 2(3.24 ft^{2})
*SA* ≈ 19 ft^{2}
Hurrah. We've succeeded. |