A metal pipe is 63cm long. Inner diameter of a cross section is 6m and the outer diameter is 8cm find:-surface area of the base a , surface area of the base b , the outer curved surface area inner curved surface area total surface area
To find the surface areas of the various parts of the metal pipe, we need to calculate the areas of different shapes involved.
First, let's determine the radius of the inner and outer diameters of the pipe:
- Inner diameter = 6 cm
- Inner radius (r1) = inner diameter / 2 = 6 cm / 2 = 3 cm
- Outer diameter = 8 cm
- Outer radius (r2) = outer diameter / 2 = 8 cm / 2 = 4 cm
Now, let's calculate the surface areas of the different parts of the pipe:
1. Surface Area of Base A (inner base):
Base A is a circle with radius r1.
Area of Base A = π * (r1)^2
= π * (3 cm)^2
2. Surface Area of Base B (outer base):
Base B is a circle with radius r2.
Area of Base B = π * (r2)^2
= π * (4 cm)^2
3. Outer Curved Surface Area:
The outer curved surface of the pipe is a cylinder with height equal to the length of the pipe and the circumference of the outer base.
Outer Curved Surface Area = 2π * r2 * h
= 2π * (4 cm) * (63 cm)
4. Inner Curved Surface Area:
The inner curved surface of the pipe is also a cylinder with height equal to the length of the pipe and the circumference of the inner base.
Inner Curved Surface Area = 2π * r1 * h
= 2π * (3 cm) * (63 cm)
5. Total Surface Area:
The total surface area of the pipe is the sum of the surface areas of the two bases and the outer and inner curved surfaces.
Total Surface Area = Surface Area of Base A + Surface Area of Base B + Outer Curved Surface Area + Inner Curved Surface Area
Now, you can calculate the values by substituting the respective values into the formulas and perform the calculations using a calculator or computer program.
area of base: pi(8^2-6^2) = 28pi
outer area: 2pi*8*63 = 1008pi
inner area: 2pi*6*63 = 756pi