Question

5 dm. Find its total surface area.
A metallic pipe is 0.7 cm thick. Inner radius of the pipe is 3.5 cm and length is
'Hint: Total surface area = Inner surface area + Outer surface area + Area of two rims)​

Answer 1

Answer:

Explanation:

Inner curved surface area = 2πrh .

Similarly, we can find the outer curved surface area of the cylindrical pipe using the outer radius, which is equal to r + thickness = 3.5+07=4.2 cm.

Height of the pipe remains the same in both the cases as it is width which is changing not height.

Outer curved surface area = 2πRh=2π(r+0.7)h

We can also observe from the diagram that the area of the rim on one side is equal to the area of the larger circle minus the area of the smaller circle. We also need to note here that there is one rim at each end so in total we have two such rims.

Area of the 2 rims = 2(πR2−πr2)=2(π(r+0.7)2−πr2)

Now to find the total surface area of a cylindrical pipe we have to equate this with the sum of inner curved surface area, outer curved surface area and twice the area of the rims. (As already discussed we have 2 such rims one at each end)

∴Total surface area = 2πrh+2π(r+0.7)h−2πr2+2π(r+0.7)2

⇒Total surface area = (3.5×50+(3.5+0.7)×50−(3.5)2+(3.5+0.7)2)2π

⇒Total surface area = (175+210−12.25+17.64)2π

⇒Total surface area = 780.78π

Now if we substitute the value of π=3.14, we get

Total surface area = 2451.65cm2

Therefore, a metallic pipe 0.7 cm thick with an inner radius of the pipe is 3.5 cm and length is 5 dm has its total surface area as 2451.65 sq. cm.