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The radius of a cylinder is 3.5 ft. The height is 14 ft. Find the surface area and volume of the cylinder to the nearest tenth of a foot. Show your work.
I NEED HELP PLS INCLUDE WORK PLS
volume of cylinder = π r^2 h
now just plug in your numbers and grind it out
surface area = 2πrh + 2π r^2
again, just work it out
IM NOT GOOD AT MATH
To find the surface area of a cylinder, you need to calculate the areas of the two bases and the lateral surface area. Let's break it down step by step:
1. Start by finding the area of one of the cylinder's bases. The formula for the area of a circle is A = πr², where A is the area and r is the radius. In this case, the radius is 3.5 ft, so the area of one base is A₁ = π × (3.5 ft)².
2. Multiply the area of one base by 2 to find the combined area of both bases. A_bases = 2 × A₁.
3. Next, calculate the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is A_lateral = 2πrh, where r is the radius and h is the height. In this case, the radius is 3.5 ft and the height is 14 ft, so the lateral surface area is A_lateral = 2π × (3.5 ft) × (14 ft).
4. Add the combined area of the bases and the lateral surface area to find the total surface area of the cylinder. A_total = A_bases + A_lateral.
To find the volume of a cylinder, you need to multiply the area of one base by the height. Here are the steps:
1. Start by finding the area of one of the cylinder's bases. We already calculated this in the previous steps as A₁ = π × (3.5 ft)².
2. Multiply the area of one base by the height to find the volume of the cylinder. V = A₁ × h.
Now, let's plug in the values and calculate the surface area and volume of the cylinder:
Step 1: Calculate the area of one base:
A₁ = π × (3.5 ft)²
≈ 38.48 ft² (round to the nearest tenth)
Step 2: Find the combined area of the bases:
A_bases = 2 × A₁
≈ 2 × 38.48 ft²
≈ 76.96 ft² (round to the nearest tenth)
Step 3: Calculate the lateral surface area:
A_lateral = 2π × (3.5 ft) × (14 ft)
≈ 2π × 3.5 ft × 14 ft
≈ 308 ft² (round to the nearest tenth)
Step 4: Find the total surface area of the cylinder:
A_total = A_bases + A_lateral
≈ 76.96 ft² + 308 ft²
≈ 384.96 ft² (round to the nearest tenth)
Step 5: Calculate the volume of the cylinder:
V = A₁ × h
≈ 38.48 ft² × 14 ft
≈ 538.72 ft³ (round to the nearest tenth)
Therefore, the surface area of the cylinder is approximately 384.96 ft² and the volume is approximately 538.72 ft³.