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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

$$\mathrm{a})\mathrm{BC}=3\mathrm{cm}$$$$\mathrm{DE}=7\mathrm{cm}$$$$\mathrm{BD}=8\mathrm{cm}$$$$\mathrm{AB}=\mathrm{x}$$$$\frac{\mathrm{AB}}{\mathrm{AD}}=\frac{\mathrm{BC}}{\mathrm{DE}}$$$$\frac{\mathrm{x}}{\mathrm{x}+8}=\frac{3}{7}$$$$7\mathrm{x}=3\mathrm{x}+24$$$$4\mathrm{x}=24$$$$\mathrm{x}=6\mathrm{cm}=\mathrm{AB}$$$$\mathrm{AD}=\mathrm{AB}+\mathrm{BD}=6+8=14\mathrm{cm}$$$$\mathrm{b})\mathrm{Volume}=\frac{1}{3}\pi ({\mathrm{DE}}^2.\mathrm{AD}-{\mathrm{BC}}^2.\mathrm{AB})$$$$=\frac{1}{3}\times 3.14\times (7^2\times 14-3^2\times 6)$$$$=661.5{\mathrm{cm}}^3=0.6615\mathrm{litre}$$$$\mathrm{c})\mathrm{AC}=\sqrt{{\mathrm{AB}}^2+{\mathrm{BC}}^2}=\sqrt{6^2+3^2}=6.7\mathrm{cm}$$$$\mathrm{AE}=\sqrt{{\mathrm{AD}}^2+{\mathrm{DE}}^2}=\sqrt{{14}^2+7^2}=15.7\mathrm{cm}$$$$\mathrm{Surface}\mathrm{area}=\pi ({\mathrm{DE}}^2+{\mathrm{BC}}^2+\mathrm{DE}.\mathrm{AE}-\mathrm{BC}.\mathrm{AC})$$$$=3.14(7^2+3^2+7\times 15.7-3\times 6.7)$$$$=464.1{\mathrm{cm}}^2$$

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

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

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