Question

What is the surface area of the cylinder with height 6 km and radius 4 km? Round your answer to the nearest thousandth.

Answer 1

251.327 km² (nearest thousandth)

Explanation:

The formula for the surface area of a cylinder is:

`\boxed{S.A. = 2\pi r^2 + 2\pi rh}`

where r is the radius and h is the height of the cylinder.

Substitute the given values of r = 4 km and h = 6 km into the formula and solve:

`\begin{aligned}S.A. &= 2\pi (4)^2 + 2\pi (4)(6)\\&=2\pi (16)+2 \pi (24)\\&=32 \pi+ 48 \pi\\&=80 \pi\\&=251.327412...\\&=251.327\; \sf km^2 \end{aligned}`

Therefore, the surface area of the cylinder with height 6 km and radius 4 km is 251.327 square kilometers, rounded to the nearest thousandth.

Answer 2

• Curved surface area is 150.796 km²,
• Total surface area is 251.327 km².

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Curved surface area of a cylinder:

• CSA = 2πrh

Substitute 6 for h and 4 for r:

• CSA = 2π(6)(4) = 150.796447372 ≈ 150.796 km² (rounded)

Total surface area adds top and bottom faces:

• TSA = 2πrh + 2πr²
• TSA = 2πr(r + h)
• TSA = 2π(4)(4 + 6) = 251.327412287 ≈ 251.327 km² (rounded)