Find the volume of a conical tin having radius of the base as 30cm and its slant height as 50cm. Also find how many such tins are required to fill 56520 cu.cm of oil .(take pie as 3.14)
Answers
Answer:
Volume of the conical tin is 6280 cubic cm.
Step-by-step explanation:
Formula used:
1.Volume of cone=\frac{1}{3}\:\pi\:r^2h=
3
1
πr
2
h cubic units
2.l^2=h^2+r^22.l
2
=h
2
+r
2
Let r, h and l be radius, height and slant height of the conical tin respectively.
Given:
Radius of the conical tin, r = 30 cm
Slant height of the conical tin, l=50 cm
\begin{gathered}l^2=h^2+r^2\\\\(50)^2=h^2+(30)^2\\\\2500=h^2+900\\\\h^2=2500-900\\\\h^2=1600\\\\h=\sqrt{1600}\\\\h=40\:cm\end{gathered}
l
2
=h
2
+r
2
(50)
2
=h
2
+(30)
2
2500=h
2
+900
h
2
=2500−900
h
2
=1600
h=
1600
h=40cm
Now,
Volume of the conical tin
\begin{gathered}=\frac{1}{3}\:\pi\:r^2h\\\\=\frac{1}{3}\:(3.14)\:(30)^2(40)\\\\=\frac{1}{3}\:(3.14)\:(30)^2(40)\\\\=\frac{1}{3}\:(3.14)\:(900)(40)\\\\=3.14*300*40\\\\=314*3*40\\\\=314*120\\\\=6280 \;cubic \:cm.\end{gathered}
=
3
1
πr
2
h
=
3
1
(3.14)(30)
2
(40)
=
3
1
(3.14)(30)
2
(40)
=
3
1
(3.14)(900)(40)
=3.14∗300∗40
=314∗3∗40
=314∗120
=6280cubiccm.
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