An iron drainage tube is in the shape of right circular cylinder in its lower part, while the upper part looks like right circular cone. The radius of the base of the cone as well as the base of the cylinder is 6 m. The cylindrical portion is 20 m tall and the conical portion is 9 m tall. Find the mass of a single tube if the 1 m weighs 7 kgs.
Answers
Answer:
Let rr cm be the radius and hh cm the height of the cylindrical part. Then, r=5cm,h=13cmr=5cm,h=13cm
Clearly radii of the spherical part and base of the conical part are also rr cm. Let {h}_{1}h
1
cm be the height, ll cm be the slant height of the conical part.
Then
{ l }^{ 2 }={ r }^{ 2 }+{ h }_{ 1 }^{ 2 }\Rightarrow l=\sqrt { { r }^{ 2 }+{ h }_{ 1 }^{ 2 } } \Rightarrow l=\sqrt { { 5 }^{ 2 }+{ 12 }^{ 2 } } =13cm\quad l
2
=r
2
+h
1
2
⇒l=
r
2
+h
1
2
⇒l=
5
2
+12
2
=13cm
Now
surface area of the toy==
curved surface area of the cylindrical part + curved surface area of hemispherical part + curved surface area of conical part
=\left( 2\pi rh+2\pi { r }^{ 2 }+\pi rl \right) { cm }^{ 2 }=(2πrh+2πr
2
+πrl)cm
2
=\pi r\left( 2h+2r+l \right) { cm }^{ 2 }=πr(2h+2r+l)cm
2
=\left\{ \cfrac { 22 }{ 7 } \times 5\times \left( 2\times 13+2\times 5+13 \right) \right\} { cm }^{ 2 }={
7
22
×5×(2×13+2×5+13) }cm
2
=770{ cm }^{ 2 }\quad =770cm
2
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