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
inner curved surface area,
outer curved surface area,
i total surface area.
Answers
EXPLANATION.
A metal pipe is 77 cm long
The inner diameter of a cross section is 4 cm.
The outer diameter being 4.4 cm.
As we know that,
Formula of :
Curved surface area of cylinder = 2πrh.
Diameter = 2 x Radius.
Using this formula in this question, we get.
Radius of inner cross section = 4/2.
Radius of inner cross section = 2 cm.
⇒ 2πr₁h.
⇒ 2 x 22/7 x 2 x 77.
⇒ 2 x 22 x 2 x 11.
⇒ 968 cm².
∴ The inner curved surface area is 968 cm².
Radius of outer cross section = 4.4/2.
Radius of outer cross section = 2.2 cm.
⇒ 2πr₂h.
⇒ 2 x 22/7 x 2.2 x 77.
⇒ 2 x 22 x 2.2 x 11.
⇒ 1064.8 cm².
∴ The outer curved surface area is 1064.8 cm².
Area of base = πr².
Area of base of outer cross section - Area of base of inner cross section.
⇒ πr₂² - πr₁².
⇒ π(r₂² - r₁²).
⇒ 22/7 x [(2.2)² - (2)²].
⇒ 22/7 x (2.2 + 2)(2.2 - 2).
⇒ 22/7 x 4.2 x 0.2.
⇒ 22 x 0.6 x 0.2.
⇒ 2.64 cm².
Area of base is 2.64 cm².
To find : Total surface area.
Total surface area = Curved surface area of inner cross section + Curved surface area of outer cross section + 2 x Area of base.
Total surface area = 968 cm² + 1064.8 cm² + 2 x 2.64 cm².
Total surface area = 968 cm² + 1064.8 cm² + 5.28 cm².
∴ Total surface area = 2038.08 cm².
EXPLANATION.
A metal pipe is 77 cm long
The inner diameter of a cross section is 4 cm.
The outer diameter being 4.4 cm.
As we know that,
Formula of :
Curved surface area of cylinder = 2πrh.
Diameter = 2 x Radius.
Using this formula in this question, we get.
Radius of inner cross section = 4/2.
Radius of inner cross section = 2 cm.
⇒ 2πr₁h.
⇒ 2 x 22/7 x 2 x 77.
⇒ 2 x 22 x 2 x 11.
⇒ 968 cm².
∴ The inner curved surface area is 968 cm².
Radius of outer cross section = 4.4/2.
Radius of outer cross section = 2.2 cm.
⇒ 2πr₂h.
⇒ 2 x 22/7 x 2.2 x 77.
⇒ 2 x 22 x 2.2 x 11.
⇒ 1064.8 cm².
∴ The outer curved surface area is 1064.8 cm².
Area of base = πr².
Area of base of outer cross section - Area of base of inner cross section.
⇒ πr₂² - πr₁².
⇒ π(r₂² - r₁²).
⇒ 22/7 x [(2.2)² - (2)²].
⇒ 22/7 x (2.2 + 2)(2.2 - 2).
⇒ 22/7 x 4.2 x 0.2.
⇒ 22 x 0.6 x 0.2.
⇒ 2.64 cm².
Area of base is 2.64 cm².
To find : Total surface area.
Total surface area = Curved surface area of inner cross section + Curved surface area of outer cross section + 2 x Area of base.
Total surface area = 968 cm² + 1064.8 cm² + 2 x 2.64 cm².
Total surface area = 968 cm² + 1064.8 cm² + 5.28 cm².
∴ Total surface area = 2038.08 cm².