Math, asked by kitu6852, 8 months ago

the top and bottom radius of frusturm are 7m and 14m and height of frusturm is 10 m find the volume and total surface area of frusturm.​

Answers

Answered by amansharma264
6

 \bf \to \: { \underline{given \div }}

 \sf \to \: top \: and \: bottom \: of \: radius \: of \: frustum \:  = 7m \: and \: 14m. \\  \\  \sf \to \: height \: of \: the \: frustum \:  = 10m.

 \bf \to \: { \underline{to \: find \div }} \\  \\  \sf \to \: 1) = volume \: of \: frustum \\  \\  \sf \to \: 2) = total \: surface \: area \: of \: frustum.

 \bf \to \:  \orange{{ \underline{step - by - step \: \:  explanation}}}

 \sf \to \:top \: of \: radius \:  =  r_{1} \:  = 7m. \\  \\   \sf \to \: bottom \: of \: radius \:  =  r_{2} \:  = 14m \\  \\   \sf \to \: height \:  = 10m \\  \\   \sf \to \: { \underline{volume \: of \: frustum \: of \: cone}} \\  \\   \sf \to \:  \dfrac{1}{3}\pi \: h \: ( r_{1} {}^{2}  +  r_{1} r_{2} \:  +  r_{2} {}^{2}   ) \\  \\   \sf \to \:  \frac{1}{3}  \times  \frac{22}{7}  \times 10 (7 \times 7 + 7 \times 14 + 14 \times 14) \\  \\   \sf \to \:  \frac{1}{3}  \times  \frac{22}{7}  \times 10(49 + 98 + 196) \\  \\   \sf \to \:  \frac{1}{3}  \times  \frac{22}{7}   \times 10 \times 343 \\  \\   \sf \to \:  \frac{1}{3}  \times  \frac{22}{ \cancel{7}} \times 10 \times  \cancel{343}  \\  \\   \sf \to \:  \frac{22 \times 10 \times 49}{3} = 3593.3m {}^{3} \\  \\   \sf \to \:  \green{{ \underline{volume \: of \: frustum \:  = 3593.3 {m}^{3}  }}}

   \sf \to \: slant \: height \: of \: frustum \: of \: cone \\  \\     \sf \to \:  \sqrt{( r_{2} \:  -  r_{1}) {}^{2}  +  {h}^{2}   }  \\  \\   \sf \to \:  \sqrt{(14 - 7) {}^{2}  + 10 {}^{2} } \\  \\   \sf \to \:  \sqrt{49 + 100}  =  \sqrt{149}   = 12.2m \\  \\   \sf \to \: { \underline{total \: surface \: area \: of \: frustum}} \\  \\  \sf \to \: \pi \: l \: ( r_{1} \:  +  r_{2} \: ) + \pi \: ( r_{1} {}^{2}  +  r_{2} {}^{2} ) \\  \\  \sf \to \:  \frac{22}{7} \times 12.2(14 + 7) +  \frac{22}{7}( {7}^{2} +  {14}^{2} ) \\  \\  \sf \to \:  \frac{22}{7} \times 12.2 \times 21 +  \frac{22}{7} \times (49 + 196) \\  \\  \sf \to \: 804.468 + 349.86 = 1154.328m {}^{2}   \\  \\  \sf \to \:  \orange{{ \underline{total \: surface \: area \: of \: frustum \:   = 1154.328 {m}^{2} }}}

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