A cylindrical piece of wood of radius 4.2 cm and length 150 cm is cut length rise into two equal pieces. Calculate the surface area of one piece
I'll use h for height, because l for length looks like the number 1.
the surface area is
two semi-circular ends: 2*(πr^2/2) = πr^2
the rectangular cut surface: 2rh
the curved surface: πrh
Now just plug and chug
45cm
3987.72
Just do the working understanding nothing
To calculate the surface area of one piece of the cylindrical wood, we need to find the lateral surface area.
The formula for lateral surface area of a cylinder is given by:
Lateral Surface Area = 2πrh
Where,
r = radius of the cylinder
h = height/length of the cylinder
In this case, we are given that the radius (r) of the cylindrical piece of wood is 4.2 cm. However, we need to find the height/length (h) of the piece after it is cut.
Since the cylindrical piece of wood is cut lengthwise into two equal pieces, the length of each piece would be half the original length. Therefore, the height/length (h) of each piece would be 150 cm ÷ 2 = 75 cm.
Now we can substitute the values into the formula to calculate the lateral surface area (SA) of one piece.
Lateral Surface Area = 2πrh
SA = 2π(4.2 cm)(75 cm)
Calculating this expression:
SA ≈ 2 × 3.14159 × 4.2 cm × 75 cm
SA ≈ 2 × 3.14159 × 4.2 × 75 cm²
SA ≈ 6.28318 × 4.2 × 75 cm²
SA ≈ 157.07964 × 4.2 cm²
SA ≈ 659.734 cm²
Therefore, the surface area of one piece of the cylindrical wood, after it is cut lengthwise, is approximately 659.734 cm².