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Question Number 47250 by Raj Singh last updated on 07/Nov/18

Answered by MJS last updated on 07/Nov/18

surface of cuboid  2×(15×10+15×5+10×5)=550  surface of cylinder (without bottom&top)  2×3.5π×5=35π  surface of bottom&top  2×(3.5)^2 π=((49)/2)π  surface of remaining body  550+35π−((49)/2)π=550+((21)/2)π ≈582.99cm^2

$$\mathrm{surface}\:\mathrm{of}\:\mathrm{cuboid} \\ $$$$\mathrm{2}×\left(\mathrm{15}×\mathrm{10}+\mathrm{15}×\mathrm{5}+\mathrm{10}×\mathrm{5}\right)=\mathrm{550} \\ $$$$\mathrm{surface}\:\mathrm{of}\:\mathrm{cylinder}\:\left(\mathrm{without}\:\mathrm{bottom\&top}\right) \\ $$$$\mathrm{2}×\mathrm{3}.\mathrm{5}\pi×\mathrm{5}=\mathrm{35}\pi \\ $$$$\mathrm{surface}\:\mathrm{of}\:\mathrm{bottom\&top} \\ $$$$\mathrm{2}×\left(\mathrm{3}.\mathrm{5}\right)^{\mathrm{2}} \pi=\frac{\mathrm{49}}{\mathrm{2}}\pi \\ $$$$\mathrm{surface}\:\mathrm{of}\:\mathrm{remaining}\:\mathrm{body} \\ $$$$\mathrm{550}+\mathrm{35}\pi−\frac{\mathrm{49}}{\mathrm{2}}\pi=\mathrm{550}+\frac{\mathrm{21}}{\mathrm{2}}\pi\:\approx\mathrm{582}.\mathrm{99cm}^{\mathrm{2}} \\ $$

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