Question

A right triangle abc with sides 5cm 12cm and 13 cm is revolved about the side 12 cm. find the volume of the solid so obtained

Answer 1

$\huge{\underline{\overline{\mid{\mathfrak{\purple{\:\: SOLUTION\:\:} \mid}}}}}$

$\pink{\bf{Given}\begin{cases}\sf{ \red{Radius\:of\: the\: triangle = }5\:cm }\\\sf{ \green{Height \:of\: the\: triangle = 12\:cm}\: }\\ </p><p>\sf{ \red{Slant\:height \:of\: the\: triangle = }13\:cm\: }\\</p><p>\sf{ \green{Volume\: of\:the\: solid = \:?} \: }\\</p><p>\end{cases}}$

$\underline{ \mathfrak{ \: \:Formula \: \: used \: \: here:- \: \: }}$

$\: \: \: \: \: \: \: \: \: \: \: \sf{Volume\: of\: solid = \dfrac{1}{3}\pi r^2h}$

$\underline{ \mathfrak{ \: Putting\:\:the\:\:values:- \: }}$

$\sf{ \longrightarrow \: Volume\: of\:the\: solid = \bigg(\dfrac{1}{3} \times \pi \times 5 \times 5 \times 12\bigg)cm^3}$

$\sf{ \longrightarrow \: Volume\: of\:the\: solid = \bigg(1 \times \pi \times 25 \times 4\bigg)cm^3}$

$\sf{ \longrightarrow \: Volume\: of\:the\: solid = \bigg(1 \times \pi \times 100\bigg)cm^3}$

$\sf{ \longrightarrow \: Volume\: of\:the\: solid = 100\: \pi\: cm^3}$

$\underline{ \mathfrak{ \: \: Therefore:- \: \: }}$

$\: \: \: \sf{\green{Volume\: of\:the\: solid = \underline{ \: 100 \: \pi \:cm^3 \: }}}$

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$\underline{ \mathfrak{ \: \: Required \: \: Diagram:- \: \: }}$

$\setlength{\unitlength}{0.99cm}\begin{picture}(6, 4)\linethickness{0.26mm}\qbezier(5.8,2.0)(5.8,2.3728)(4.9799,2.6364)\qbezier(4.9799,2.6364)(4.1598,2.9)(3.0,2.9)\qbezier(3.0,2.9)(1.8402,2.9)(1.0201,2.6364)\qbezier(1.0201,2.6364)(0.2,2.3728)(0.2,2.0)\qbezier(0.2,2.0)(0.2,1.6272)(1.0201,1.3636)\qbezier(1.0201,1.3636)(1.8402,1.1)(3.0,1.1)\qbezier(3.0,1.1)(4.1598,1.1)(4.9799,1.3636)\qbezier(4.9799,1.3636)(5.8,1.6272)(5.8,2.0)\put(0.2,2){\line(1,0){2.8}}\put(3.05,4){\sf{h = 10cm}}\put(3,2){\line(0,2){4.5}}\put(1.5,1.7){\sf{r = 5cm}}\qbezier(.2,2.05)(.7,3)(3,6.5)\qbezier(5.8,2.05)(5.3,3)(3,6.5)\put(0,4){\sf{l = 13cm}}\put(3,2.02){\circle*{0.15}}\put(2.7,2){\dashbox{0.01}(.3,.3)}\end{picture}$

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