How many times will the surface area of a regular octagonal prism increase if all its edges are increased by 1.5 times?
| September 30, 2021 | education
a1 = 1.5 * a.
h1 = 1.5 * h
S1 / S2 -?
The surface area S of a regular octagonal prism is determined by the formula: S = 2 * S main + 8 * S side.
The base of a regular octagonal prism is a regular octagon.
The area of a regular octagon is determined by the formula: Sb = 2 * a ^ 2 * (1 + √2).
Sside = a * h.
S1 = 2 * Sbok1 + 8 * Sbok1.
Sosn1 = 2 * a1 ^ 2 * (1 + √2) = 2 * (1.5 * a) ^ 2 * (1 + √2) = 2.25 * 2 * a ^ 2 * (1 + √2) = 2.25 * Sb.
S side1 = a1 * h1 = 1.5 * a * 1.5 * h = 2.25 * a * h = 2.25 * S side.
S1 = 2 * Sbn1 + 8 * Sbok1 = 2 * 2.25 * Sbn + 8 * 2.25 * Sbok = 2.25 * (2 * Sbn + 8 * Sbok) = 2.25 * S.
Answer: the surface area of a regular octagonal prism will increase 2.25 times: S1 = 2.25 * S.
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