Two open cylindrical tanks are geometrically similar. The smaller has internal radius 3 m and intern

Question

Two open cylindrical tanks are geometrically similar. The smaller has internal radius 3 m and internal height 8 m; every length of the larger is doubled. Wall thickness is negligible. The outside curved surface and the bottom are coated, but there is no top. Coating costs the same per square metre. Find the coating-area ratio, smaller : larger.[1] Find the capacity ratio, smaller : larger.[1] Which tank has the lower coating cost per cubic metre of capacity? State the factor and explain.[2]

Accepted Answer

(a) $1:4$. (b) $1:8$. (c) The larger tank, at half the cost per unit capacity.

Capacity gained for coating cost

Capacity gained for coating cost

Solution:

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