If the circumference of a conical wooden piece is 484 cm. then find it

1.	If the circumference of a conical wooden piece is 484 cm. then find its volume when its height is 105 cm
Answer» en Circumference of the BASE of the CONE= 484cm Height = 105 cm To Find Volume Of Cone Solution $~~~~~~~~{\pink{\sf Circumference \: of \: Circle = 2πr}}$ ${\implies\sf 484 = 2 \times \dfrac{22}{7} \times r}$ ${\implies\sf r = \dfrac{484 \times 7}{ 2\times 22}}$ ${\implies\sf r = \dfrac{3388}{ 44}}$ $~~~~~~~{\sf r = 77cm}$ $~~~~~~~~~{\pink{\sf \: volume \: of\: a\: conical\: wooden\: piece\: \: = \: \dfrac{1}{3} \pi {r}^{2} h}}$ ${\implies\sf \: volume \: of\: a\: conical\: wooden\: piece\: \: = \: \dfrac{1}{3} \times \dfrac{22}{7} \times {77}^{2} \times 105}$ ${\implies\sf \: volume \:of\: a\: conical\: wooden\: piece\: \: = \: \dfrac{1}{ \cancel{3}} \times \dfrac{22}{7} \times {5929}\times \cancel{105}^{35} }$ ${\implies\sf \: volume \: of\: a\: conical\: wooden\: piece\: \: = \dfrac{22}{7} \times5929 \times35}$ ${\implies\sf \: volume \: of\: a\: conical\: wooden\: piece\: \: = {22} \times847 \times35}$ $~~~~~~~~~~~~~\underline{\boxed{\sf \: volume \: of\: a\: conical\: wooden\: piece\: \: = 652190 \: cm^{3}} }\\\\\\\\$ Figure Of Cone $\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{r}}\put(9.5,10){\sf{h}}\end{picture}$

If the circumference of a conical wooden piece is 484 cm. then find its volume when its height is 105 cm

Answer»

Circumference of the BASE of the CONE= 484cm
Height = 105 cm

To Find

Volume Of Cone

Solution

$~~~~~~~~{\pink{\sf Circumference \: of \: Circle = 2πr}}$

${\implies\sf 484 = 2 \times \dfrac{22}{7} \times r}$

${\implies\sf r = \dfrac{484 \times 7}{ 2\times 22}}$

${\implies\sf r = \dfrac{3388}{ 44}}$

$~~~~~~~{\sf r = 77cm}$

$~~~~~~~~~{\pink{\sf \: volume \: of\: a\: conical\: wooden\: piece\: \: = \: \dfrac{1}{3} \pi {r}^{2} h}}$

${\implies\sf \: volume \: of\: a\: conical\: wooden\: piece\: \: = \: \dfrac{1}{3} \times \dfrac{22}{7} \times {77}^{2} \times 105}$

${\implies\sf \: volume \:of\: a\: conical\: wooden\: piece\: \: = \: \dfrac{1}{ \cancel{3}} \times \dfrac{22}{7} \times {5929}\times \cancel{105}^{35} }$

${\implies\sf \: volume \: of\: a\: conical\: wooden\: piece\: \: = \dfrac{22}{7} \times5929 \times35}$

${\implies\sf \: volume \: of\: a\: conical\: wooden\: piece\: \: = {22} \times847 \times35}$

$~~~~~~~~~~~~~\underline{\boxed{\sf \: volume \: of\: a\: conical\: wooden\: piece\: \: = 652190 \: cm^{3}} }\\\\\\\\$

Figure Of Cone

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{r}}\put(9.5,10){\sf{h}}\end{picture}$