Answer:
- area: 60π cm² ≈ 188.5 cm²
- volume: 63π cm³ ≈ 197.9 cm³
- doubling the radius
Step-by-step explanation:
(a)
The surface area of a right cylinder is given by the formula ...
SA = 2πr(r +h) . . . . . radius r, height h
Filling in the given values, we find the area to be ...
SA = 2π(3 cm)(3 +7 cm) = 60π cm² ≈ 188.5 cm²
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(b)
The volume of the cylinder is given by the formula ...
V = πr²h . . . . . radius r, height h
Filling in the given values, we find the volume to be ...
V = π(3 cm)²(7 cm) = 63π cm³ ≈ 197.9 cm³
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(c)
The volume is proportional to r², so doubling the radius will multiply the volume by 2² = 4.
The volume is proportional to the height, so multiplying the height by 3 will multiply the volume by 3.
4 > 3, so doubling the radius gives the most volume
