A cylinder has a height of 15 feet and a radius of 4 feet. Solve for the total surface area of the cylinder. Use 3.14 for π and round to the nearest tenth.(1 point)
The formula for the total surface area of a cylinder is given by:
S = 2πr(r+h)
where r is the radius and h is the height.
Plugging in the values:
S = 2 * 3.14 * 4 * (4+15)
S = 2 * 3.14 * 4 * 19
S = 3.14 * 8 * 19
S = 3.14 * 152
S ≈ 478.88
So, the total surface area of the cylinder is approximately 478.9 square feet.
thats wrong
I apologize for the mistake. Let's solve the problem correctly.
The formula for the total surface area of a cylinder is given by:
S = 2πrh + 2πr²
where r is the radius and h is the height.
Plugging in the given values:
S = 2 * 3.14 * 4 * 15 + 2 * 3.14 * 4²
S = 2 * 3.14 * 4 * 15 + 2 * 3.14 * 16
S = 100.48 + 100.48
S ≈ 200.96
So, the total surface area of the cylinder is approximately 200.96 square feet.
i thought it was 477.3
Apologies for the confusion. Let's solve the problem again.
The formula for the total surface area of a cylinder is given by:
S = 2πrh + 2πr²
where r is the radius and h is the height.
Plugging in the given values:
S = 2 * 3.14 * 4 * 15 + 2 * 3.14 * 4²
S = 2 * 3.14 * 4 * 15 + 2 * 3.14 * 16
S = 376.8 + 100.48
S ≈ 477.28
So, the correct answer is approximately 477.3 square feet.
To find the total surface area of a cylinder, you need to add the areas of its two bases and the lateral surface area.
1. Start by finding the area of the two bases:
- The base of a cylinder is a circle, and the formula to find its area is: A = π * r^2, where "A" is the area, and "r" is the radius.
- Plug in the given radius of 4 feet: A(base) = 3.14 * 4^2.
- Calculate the area of one base: A(base) = 3.14 * 16.
- The cylinder has two bases, so multiply the area by 2 to get the total area of both bases: A(bases) = 2 * 3.14 * 16.
2. Next, find the lateral surface area:
- The lateral surface area is the curved surface of the cylinder, excluding the bases.
- The formula to find the lateral surface area is: A(lateral) = 2 * π * r * h, where "h" is the height of the cylinder.
- Plug in the given radius of 4 feet and the height of 15 feet: A(lateral) = 2 * 3.14 * 4 * 15.
3. Add the areas of the two bases and the lateral surface area:
- Total Surface Area (SA) = A(bases) + A(lateral).
Now, let's calculate the values and get the final rounded answer.
A(bases) = 2 * 3.14 * 16 = 100.48 (rounded to the nearest hundredth).
A(lateral) = 2 * 3.14 * 4 * 15 = 377.04 (rounded to the nearest hundredth).
SA = A(bases) + A(lateral) = 100.48 + 377.04 = 477.52 (rounded to the nearest tenth).
Therefore, the total surface area of the given cylinder is approximately 477.5 square feet.