Question

The height of a cone is 27. If its volume is 1570, find the radius of its base.

Answer 1

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0) \thicklines\qbezier(1,0)(1.9,1)(3,0)\qbezier(1,0)(1.9, - 1)(3,0)\put(0.9,0){ \line(1,3){1}}\put(2.9,0){ \line( - 1,3){1}} \put(3,0){ \vector( 0,1){3}}\put( 3,0){ \vector( 0, - 1){.1}} \put(3.1,1.5){ \bf 27 \ cm }\put(0.6, - 1.4){ \boxed{ \bf{volume =1570 \ {cm}^{3} }} }\put(1,0){\vector(1,0){1}}\put(2,0){\vector( - 1,0){1}}\put(1.6,0.1){ \bf r }\end{picture}$

${ \tt { \large \underline {given}}}$

${ \rm{the \: height \: of \: cone \: is = 27 \: cm}}$

b${ \rm{and \: its \: volume \: is = 1570 {cm}^{3} }}$

${ \tt { \large \underline {to \: find}}}$

${ \rm{ \to the \: radius \: of \: the \: base \: of \: cone}}$

${ \tt { \large \underline {solution}}}$

${ \rm{ \frac{1}{3} \pi {r}^{2} h = volume}}$

${ \rm{ \implies \frac{1}{3} \times \frac{22}{7} \times {r}^{2} \times 27 = 1570}}$

${ \rm{ \implies {r}^{2} = \frac{1570 \times 3 \times 7}{1 \times 22 \times 27} }}$

${ \rm{ {r}= 12 .90cm}}$

${ \rm{ \large so \: the \: value \: of \: r = 12.90cm}}$

──────────────────────────

${ \tt{ \large \underline \bold{more \: info}}}$

${ \rm{(i)volume = \frac{1}{3} \pi {r}^{2} h}}$

${ \rm{(ii)curve \: surface \: area = \pi rl}}$

${ \rm{total \: surface \: area = \pi r(l + r)}}$