Question-14020

Question Number 14020 by tawa tawa last updated on 26/May/17

Answered by sandy_suhendra last updated on 26/May/17

Commented by sandy_suhendra last updated on 26/May/17

a) BC = 3 cm DE = 7 cm BD = 8 cm AB = x ((AB)/(AD)) = ((BC)/(DE)) (x/(x+8)) = (3/7) 7x = 3x+24 4x = 24 x = 6 cm = AB AD = AB+BD = 6+8 = 14 cm b)Volume = (1/3)π ( DE^2 .AD − BC^2 .AB) = (1/3)×3.14×(7^2 ×14−3^2 ×6) = 661.5 cm^3 = 0.6615 litre c)AC = (√(AB^2 +BC^2 )) = (√(6^2 +3^2 )) = 6.7 cm AE = (√(AD^2 +DE^2 )) = (√(14^2 +7^2 )) = 15.7 cm Surface area = π(DE^2 +BC^2 +DE.AE−BC.AC) = 3.14(7^2 +3^2 +7×15.7−3×6.7) = 464.1 cm^2

$$\left.\mathrm{a}\right)\:\mathrm{BC}\:=\:\mathrm{3}\:\mathrm{cm} \\ $$$$\mathrm{DE}\:=\:\mathrm{7}\:\mathrm{cm} \\ $$$$\mathrm{BD}\:=\:\mathrm{8}\:\mathrm{cm} \\ $$$$\mathrm{AB}\:=\:\mathrm{x} \\ $$$$\frac{\mathrm{AB}}{\mathrm{AD}}\:=\:\frac{\mathrm{BC}}{\mathrm{DE}} \\ $$$$\frac{\mathrm{x}}{\mathrm{x}+\mathrm{8}}\:=\:\frac{\mathrm{3}}{\mathrm{7}} \\ $$$$\mathrm{7x}\:=\:\mathrm{3x}+\mathrm{24} \\ $$$$\mathrm{4x}\:=\:\mathrm{24} \\ $$$$\mathrm{x}\:=\:\mathrm{6}\:\mathrm{cm}\:=\:\mathrm{AB} \\ $$$$\mathrm{AD}\:=\:\mathrm{AB}+\mathrm{BD}\:=\:\mathrm{6}+\mathrm{8}\:=\:\mathrm{14}\:\mathrm{cm} \\ $$$$\left.\mathrm{b}\right)\mathrm{Volume}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi\:\left(\:\mathrm{DE}^{\mathrm{2}} .\mathrm{AD}\:−\:\mathrm{BC}^{\mathrm{2}} .\mathrm{AB}\right)\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{3}}×\mathrm{3}.\mathrm{14}×\left(\mathrm{7}^{\mathrm{2}} ×\mathrm{14}−\mathrm{3}^{\mathrm{2}} ×\mathrm{6}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{661}.\mathrm{5}\:\mathrm{cm}^{\mathrm{3}} \:=\:\mathrm{0}.\mathrm{6615}\:\mathrm{litre} \\ $$$$\left.\mathrm{c}\right)\mathrm{AC}\:=\:\sqrt{\mathrm{AB}^{\mathrm{2}} +\mathrm{BC}^{\mathrm{2}} }\:=\:\sqrt{\mathrm{6}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} }\:=\:\mathrm{6}.\mathrm{7}\:\mathrm{cm} \\ $$$$\mathrm{AE}\:=\:\sqrt{\mathrm{AD}^{\mathrm{2}} +\mathrm{DE}^{\mathrm{2}} }\:=\:\sqrt{\mathrm{14}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}} }\:=\:\mathrm{15}.\mathrm{7}\:\mathrm{cm} \\ $$$$\mathrm{Surface}\:\mathrm{area}\:=\:\pi\left(\mathrm{DE}^{\mathrm{2}} +\mathrm{BC}^{\mathrm{2}} +\mathrm{DE}.\mathrm{AE}−\mathrm{BC}.\mathrm{AC}\right)\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{3}.\mathrm{14}\left(\mathrm{7}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\mathrm{7}×\mathrm{15}.\mathrm{7}−\mathrm{3}×\mathrm{6}.\mathrm{7}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{464}.\mathrm{1}\:\mathrm{cm}^{\mathrm{2}} \\ $$

Commented by tawa tawa last updated on 26/May/17

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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