Question

guided practice surface areas of prisms and cylinders what is the surface area of the cylinder? round your answer to the nearest whole number. use 3.14 for π. type your answer and then click or tap done. (diagram of a cylinder with radius 4 ft and height 7 ft)

Explanation:

Step1: Identify radius and height

Radius $r = \frac{4}{2} = 2$ ft, height $h = 7$ ft

Step2: Calculate surface area

Surface area formula: $2\pi r(r + h)$
Substitute values: $2×3.14×2×(2 + 7)$
Simplify: $12.56×9 ≈ 113.04$? No, wait—wait, diameter is 4 ft, so radius 2 ft. Lateral surface area: $2\pi rh = 2×3.14×2×7 = 87.92$. Two circular areas: $2×\pi r² = 2×3.14×4 = 25.12$. Total: $87.92 + 25.12 = 113.04$? Wait, no, maybe I misread—wait the image says diameter 4 ft, height 7 ft. Correct total surface area: $2\pi r² + 2\pi rh = 2×3.14×2² + 2×3.14×2×7 = 25.12 + 87.92 = 113.04$, rounded to nearest whole number is 113. Wait, maybe I made a mistake earlier. Oh right, radius is half diameter: 4/2=2. So yes, total surface area is 113 ft².

Wait, let me recalculate:
Circular area: $\pi r² = 3.14×2² = 12.56$. Two circles: $2×12.56 = 25.12$.
Lateral surface area: $2\pi rh = 2×3.14×2×7 = 87.92$.
Total: $25.12 + 87.92 = 113.04 ≈ 113$.

So the correct answer is 113.

Step1: Find radius

Radius $r = \frac{4}{2} = 2$ ft

Step2: Calculate two circular areas

$2×\pi r² = 2×3.14×2² = 25.12$ ft²

Step3: Calculate lateral surface area

$2\pi rh = 2×3.14×2×7 = 87.92$ ft²

Step4: Sum for total surface area

$25.12 + 87.92 = 113.04 ≈ 113$ ft²

Answer:

138 ft²