Both bases are circles with an isosceles triangle cut out of them.
- The areas of the circles (each with a radius of 6) is 36π
- For isosceles triangles, the base is 8, and the altitude will hit the midpoint, creating two smaller right triangles, each with a leg of 4 and a hypotenuse of 5. Using Pythagorean Theorem, we get the altitude is 3. Using that with the area formula: 1/2(8)(3)=12
- So base areas are each 36π-12
The cylinder has a lateral area of circumference x height = 12π(45) = 540π
The surface area is the sum of all areas, so 540π + 36π-12 + 36π-12 = 612π-24
William W.
You mention removing 12.5 square units from the top and bottom. Shouldn't this be 12? The height of the triangle would be 3 (the median splits the base of 8 in half creating a 3-4-5 right triangle). A = (1/2)(8)(3) = 1207/28/25