Final answer:
The total surface area of a right cylinder with a radius of 3 inches and a height of 17 inches, rounded to the nearest tenth, is 376.9 square inches. This is calculated by finding the areas of the two circular bases and the rectangular side wrap, and summing them.
Step-by-step explanation:
To find the total surface area of a right cylinder, you need to calculate the area of the two circular bases and the area of the rectangular wrap that constitutes the side of the cylinder. The formula for the area of a circle is A = πr², where 'A' is the area and 'r' is the radius of the circle. The area of the side can be found by multiplying the circumference of the base by the height of the cylinder, so the side area formula is Circumference × Height, where the circumference is 2πr.
For a cylinder with a radius of 3 inches and a height of 17 inches, the calculations would be as follows:
- Base Area (Two circles): 2 × (π × 3²) = 2 × (π × 9)
- Side Area (Rectangular wrap): 2π × 3 × 17
Summing these two areas gives us the total surface area of the cylinder:
Total Surface Area = 2 × (π × 9) + 2π × 3 × 17
Calculating this using π ≈ 3.1415927... and rounding to the nearest tenth yields:
Total Surface Area ≈ 2 × (3.1415927 × 9) + 2× 3.1415927 × 3 × 17 ≈ 56.5 + 320.4 ≈ 376.9 square inches.
Thus, the total surface area of the cylinder to the nearest tenth is 376.9 square inches.