Answer:
The surface area is about 1000.1 in.^2
Sacha likely though that the formula for surface area was 2πr² + 2πrh and though it was simply 2πrh, since 2(3.14)(6.5)(18) = 734.76, which is 734.8 when rounded to the nearest tenth.
Explanation:
One of the formulas we can use for surface area of a cylinder is
SA = 2πr² + 2πrh, where
- SA is the surface area in square units,
- r is the radius of the cylinder's circular base,
- and h is the height.
Step 1: We already know that the height of the cylinder is 18 in., but we're not given the radius.
- However, we're given that the diameter of the cylinder's circular base is 13 in.
- We know that the diameter is 2 * the radius.
- Thus, r = d/2 and since d is 13 r = 13/2 in
- Since 13/2 as a regular number is 6.5, we can use 6.5 since we're already using 3.14
Step 2: Now we can find the surface area of the cylinder by plugging in 3.14 for π, 6.5 for r, and 18 for h and simplifying:
SA = 2(3.14)(6.5)^2 + 2(3.14)(6.5)(18)
SA = 6.28(42.25) + 6.28(117)
SA = 265.33 + 734.76
SA = 1000.09
SA = 1000.1 in^2
Thus, the surface area is about 1000.1 in^2
Step 3: Sacha likely though that the formula for surface area was 2πr² + 2πrh and though it was simply 2πrh, since 2(3.14)(6.5)(18) = 734.76, which is 734.8 when rounded to the nearest tenth.