Question

an iron right circular cone of diameter 8cm and height 12cm is melted and recast into spherical lead shots each of radius 0.4 cm.how many lead shots can be made?​

Answer 1

DIAGRAM :

$\longrightarrow \sf\: CONE$

$\setlength{\unitlength}{1.8cm}\begin{picture}(16,4)\thicklines\put(8,1){\line(1,0){1}}\put(8,1){\line(1,2){1}}\put(10,1){\line(-1,2){1}}\put(9.03,1.8){\sf{12 cm}}\put(9,1){\line(0,2){2}}\put(8.4,0.83){\sf{4 cm}}\qbezier(8,1)(9,1.5)(10,1)\qbezier(8,1)(9,0.4)(10,1)\end{picture}$

$\longrightarrow \sf\: SPHERICAL\:LEAD\:SHOTS$

$\setlength{\unitlength}{1mm}\begin{picture}(50,55)\thicklines\qbezier(25.000,10.000)(33.284,10.000)(39.142,15.858)\qbezier(39.142,15.858)(45.000,21.716)(45.000,30.000)\qbezier(45.000,30.000)(45.000,38.284)(39.142,44.142)\qbezier(39.142,44.142)(33.284,50.000)(25.000,50.000)\qbezier(25.000,50.000)(16.716,50.000)(10.858,44.142)\qbezier(10.858,44.142)( 5.000,38.284)( 5.000,30.000)\qbezier( 5.000,30.000)( 5.000,21.716)(10.858,15.858)\qbezier(10.858,15.858)(16.716,10.000)(25.000,10.000)\put(25,30){\line(5,0){20}}\put(25,30){\circle*{1}}\put(29,26){\sf\large{0.4 mm}}\end{picture}$

$\rule{300}{2}$

GIVEN :

• Diameter of right circular cone= 8 cm
• Height of circular cone = 12 cm
• Radius of spherical lead shots = 4mm

We know that $\boxed{\sf Radius=\frac{Diameter}{2}}$

Radius of Cone = $\frac{8}{2}$= 4cm.

LET :

• Radius of cone be r.
• Height of cone be h.
• Radius of spherical lead shots be r'.

Now, we know that, 10mm = 1 cm.

$\longrightarrow \sf\: 4mm= \frac{4}{10}cm$

$\boxed{\sf \:Volume\:of\:right\:circular\:cone\:=\:n \times (number\:of\:spherical\:lead\:shots)}$

$\longrightarrow \sf\: \frac{1}{3}\pi{r}^{2}h= n \times \frac{4}{3}\pi{r'}^{3}\\ \\ \longrightarrow \sf\: n = \frac{\frac{1}{3}\pi{r}^{2}h}{\frac{4}{3}\pi{r'}^{3}}$

$\longrightarrow \sf\: n=\frac{1}{3}{(4)}^{2} \times 12 \times \frac{3}{4} \times {\frac{10}{4}}^{3}$

$\\ \longrightarrow \sf\: n = 3\times5\times5\times10 \\ \\ \longrightarrow \sf\: n = 750 \:leads\:shots$

Number of leads shots = $\boxed{\sf 750}$