Surface area and Volume ( Part – 7 )

1. A metal pipe is 63 cm long . The inner diameter of a cross section is 4 cm , the outer diagram being 4.4 cm . Finds its

a). Inner curved surface area ,

b). Outer curved surface area ,

c). total surface area

Sol. a). radius of metal pipe r = 4 / 2 cm = 2 cm and height h = 63 cm

Inner curved surface area of pipe = 2 ∏ r h

Inner curved surface area of pipe = 2 * 22 / 7 * 2 * 63 cm^2

Inner curved surface area of pipe = 44 * 18 cm^2

Inner curved surface area of pipe = 792 cm^2

b). Outer radius of pipe R = 4.4 / 2 = 2.2 cm and height h = 63 cm

Outer curved surface area of pipe = 2 ∏ R h

Outer curved surface area of pipe = 2 * 22 / 7 * 2.2 * 63 cm^2

Outer curved surface area of pipe = 44 * 19.8 cm^2

Outer curved surface area of pipe = 871.2 cm^2

c). Inner radius of pipe r = 2 cm , outer radius R = 2.2 cm and height h = 63 cm

Area of upper ring of pipe = ∏ ( R^2 – r^2 )

Area of upper ring of pipe = ∏ ( 2.2^2 – 2^2 )

Area of upper ring of pipe = ( 22 / 7 ) ( 4.84 – 4 )

Area of upper ring of pipe = ( 22 * 0.12 )

Area of upper ring of pipe = 2.64 cm^2

Area of lower ring of pipe = 2.64 cm^2

Total surface area of pipe = Inner curved surface area + Outer surface area + Area of upper ring + Area of lower ring

Total surface area of pipe = 792 + 871.2 + 2.64 + 2.64 cm^2 = 1668.48 cm^2

Hence , the total surface area of pipe is 1668.48 cm^2 .

maths ncert solutions

2. A metal pipe is 70 cm long . The inner diameter of a cross section is 4 cm , the outer diagram being 4.4 cm . Finds its

a). Inner curved surface area ,

b). Outer curved surface area ,

c). total surface area

Sol. a). radius of metal pipe r = 4 / 2 cm = 2 cm and height h = 70 cm

Inner curved surface area of pipe = 2 ∏ r h

Inner curved surface area of pipe = 2 * 22 / 7 * 2 * 70 cm^2

Inner curved surface area of pipe = 44 * 20 cm^2

Inner curved surface area of pipe = 880 cm^2

b). Outer radius of pipe R = 4.4 / 2 = 2.2 cm and height h = 70 cm

Outer curved surface area of pipe = 2 ∏ R h

Outer curved surface area of pipe = 2 * 22 / 7 * 2.2 * 70 cm^2

Outer curved surface area of pipe = 44 * 22 cm^2

Outer curved surface area of pipe = 968 cm^2

c). Inner radius of pipe r = 2 cm , outer radius R = 2.2 cm and height h = 70 cm

Area of upper ring of pipe = ∏ ( R^2 – r^2 )

Area of upper ring of pipe = ∏ ( 2.2^2 – 2^2 )

Area of upper ring of pipe = ( 22 / 7 ) ( 4.84 – 4 )

Area of upper ring of pipe = ( 22 * 0.12 )

Area of upper ring of pipe = 2.64 cm^2

Area of lower ring of pipe = 2.64 cm^2

Total surface area of pipe = Inner curved surface area + Outer surface area + Area of upper ring + Area of lower ring

Total surface area of pipe = 880 + 968 + 2.64 + 2.64 cm^2 = 1853.28 cm^2

Hence , the total surface area of pipe is 1853.28 cm^2 .

Milan Tomic

Hi. I’m Designer of Blog Magic. I’m CEO/Founder of ThemeXpose. I’m Creative Art Director, Web Designer, UI/UX Designer, Interaction Designer, Industrial Designer, Web Developer, Business Enthusiast, StartUp Enthusiast, Speaker, Writer and Photographer. Inspired to make things looks better.