If the surface area of the cone shown below is 628.32m2, find its volume.
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Answer:
Solution given:
diameter [d]=16m
radius [r]=8m
let slant height =l
surface area =628.32m²
πr(r+l)=628.32m²
π×8(8+l)=628.32
8+l=628.32/(8π)
8+l=25
l=25-8
l=17m
now
height of cone [h]=√{17²-8²}=15m
Again
Volume of cone =⅓πr²h=⅓×π×8²×15=320π 0r 1005.31m³
The required volume is 320π 0r 1005.31m³
The Volume of the given Cone is: 1005.469 cubic. cm.
V=1005.469 cubic. cm.
The volume of a 3 -dimensional solid is the amount of space it occupies.
The volume V of a cone with radius r is one-third the area of the base B times the height h .
V= [tex]\frac{1}{3} \pi r^{2} h[/tex]
Surface area of cone= 628.32
[tex]\pi r(l+r)[/tex]= 628.32
3.14 x 8 (l + 8)= 628.32
l+8= 25.01
l= 17.01 cm
height= 15.01 cm
Now volume of cone,
V= [tex]\frac{1}{3} \pi r^{2} h[/tex]
= [tex]\frac{1}{3} *3.14 *8^{2}* 15.01[/tex]
=1005.469 cubic. cm.
volume of cone, V= 1005.469 cubic. cm.
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