The largest possible right circular cylinder | vedclass

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Question

(B) Edge of the cube $a = 7 \, cm$.
$Quantity \, I$: Volume of the cube left over.
Volume of cube $= a^3 = 7^3 = 343 \, cm^3$.
Volume of the larges

Vedclass · Accepted Answer

Quantity $I < $ Quantity $II$

Vedclass · Answer

(B) Edge of the cube $a = 7 \, cm$.
$Quantity \, I$: Volume of the cube left over.
Volume of cube $= a^3 = 7^3 = 343 \, cm^3$.
Volume of the largest cylinder $= \pi r^2 h = \pi (3.5)^2 (7) = \frac{22}{7} 	imes 12.25 	imes 7 = 269.5 \, cm^3$.
Volume left $= 343 - 269.5 = 73.5 \, cm^3$.
$Quantity \, II$: Surface area of the cube remaining.
Original surface area $= 6a^2 = 6(49) = 294 \, cm^2$.
When the cylinder is cut,two circular faces are removed from the top and bottom faces of the cube,but the curved surface area of the cylinder is exposed.
Remaining surface area $= (6a^2 - 2 \pi r^2) + 2 \pi r h = 294 - 2(\frac{22}{7})(3.5)^2 + 2(\frac{22}{7})(3.5)(7) = 294 - 77 + 154 = 371 \, cm^2$.
Comparing magnitudes: $73.5 < 371$,therefore $Quantity \, I < Quantity \, II$.

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