Question

A metal pipe is 77 cm long. The inner diameter of a cross
section is 4 cm, the outer diameter being 4.4 cm
(see Fig. 13.11). Find its
(i) inner curved surface area,
(ii) outer curved surface area,
(iii) total surface area.
Fig. 13.11​

Answer 1

Step-by-step explanation:

Given:-

A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm

To find:-

Find its

(i) inner curved surface area,

(ii) outer curved surface area,

(iii) total surface area.

Solution:-

Length of the metal pipe = 77cm

Height of the metal pipe (h)=77cm

Diameter of the inner pipe = 4 cm

Radius of the inner pipe (r)=diameter/2

Radius of the inner pipe = 4/2 = 2 cm

Let r = 2 cm

Diameter of the outer pipe = 4.4 cm

Radius of the outer pipe(R)=4.4/2 = 2.2 cm

Let R = 2.2 cm

I) Curved Surface Area of a Cylinder =

2πrh sq.units

Inner Curved Surface Area of the pipe

=>2×(22/7)×2×77 sq.cm

=>(2×22×2×77)/7 sq.cm

=>2×22×2×11 sq.cm

=>968 sq.cm ---------------(1)

Inner Curved Surface Area of the cylindrical pipe = 968 sq.cm

ii) Outer Curved Surface Area of the pipe

=2πRh sq.units

=>2×(22/7)×2.2×77 sq.cm

=>(2×22×2.2×77)/7 sq.cm

=>2×22×2.2×11 sq.cm

=>1064.8 sq.cm------------(2)

The base of the cylinder is a circle

The base of cylindrical pipe is a ring shaped figure

Area of the base = Area of the top

= π(R+r)(R-r) sq.units

Here , R = 2.2 cm and r = 2 cm

=>(22/7)(2.2+2)(2.2-2) sq.cm

=>(22/7)(4.2)(0.2) sq.cm

=>(22×4.2×0.2)/7 sq.cm

=>22×0.6×0.2 sq.cm

=>2.64 sq.cm

Area of the base = 2.64 sq.cm------------(3)

Area of the top = 2.64 sq.cm-------------(4)

iii) Total Surface Area of the given cylindrical pipe

=Inner Curved Surface Area+ Outer Curved surface Area+Area of the base +Area of the top

From (1),(2),(3)&(4)

=>TSA = 968+1064.8+2.64+2.64 sq.cm

TSA = 2038.08 sq.cm

Answer:-

i)Inner Curved Surface Area of the cylindrical pipe = 968 sq.cm

ii)Outer Curved Surface Area of the pipe

=1064.8 sq.cm

iii)Area of the base = 2.64 sq.cm

iv)Area of the top = 2.64 sq.cm

v)Total Surface Area of the given cylindrical pipe =

2038.08 sq.cm

Used formulae:-

• Curved Surface Area of a Cylinder =
• 2πrh sq.units
• Area of the base = Area of the top of a cylindrical pipe = Area of the ring = π(R+r)(R-r) sq.units
• Total Surface Area of the given cylindrical pipe=Inner Curved Surface Area+ Outer Curved surface Area+Area of the base +Area of the top