Question

a metal pipe is 77 cm long, the inner diameter of the cross- section is 4 cm and the outer diameter is 4.4cm. find the 1. inner curved surface area2. outer curved surface area3. total surface area

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Answer 1

Answer:

The inner radius, outer radius, and height of the cylinder are r, R, and h respectively.

Inner curved surface area = 2πrh

Outer curved surface area = 2πRh

Length of the pipe, h = 77 cm

Inner radius(r) of the pipe and outer radius(R) of the pipe are:

r = 4/2 cm = 2 cm

R = 4.4/2 cm = 2.2 cm

i) Inner curved surface area = 2πrh

= 2 × 22/7 × 2 cm × 77 cm

= 968 cm²

ii) Outer curved surface area = 2πRh

= 2 × 22/7 × 2.2 cm × 77 cm

= 1064.8 cm²

iii) The total surface area of the pipe can be obtained by adding the inner and outer curved surface areas along with the area of both the circular ends.

We can find the area of circular ends by subtracting the area of the inner circle from the outer circle area.

Area of both the circular ends of the pipe = 2 π (R² - r²)

TSA of pipe = CSA of inner surface + CSA of outer surface + Area of both the circular ends of the pipe

Hence, TSA of the pipe = 2πrh + 2πRh + 2π(R² - r²)

Now, area of both the circular ends of the pipe = 2π(R² - r²)

= 2 × 22/7 × [(2.2 cm)² - (2 cm)²]

= 2 × 22/7 × [4.84 cm² - 4 cm²]

= 2 × 22/7 × 0.84 cm²

= 5.28 cm²

Total surface area = 2πrh + 2πRh + 2π (R² - r²)

= 968 cm² + 1064.8 cm² + 5.28 cm²  [Since, Inner curved surface area = 968 cm², Outer curved surface area = 1064.8 cm²]

= 2038.08 cm²

Answer 2

Step-by-step explanation:

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case