calculate the total surface area of a closed cylinder with base radius 3 whole number 1/3 and height, 5cm. [Take n=1/7]
AAAaannndd the bot gets it wrong yet again!
2πr(r+h) = 2π(3 1/3)(3 1/3 + 5) = 500/9 π ≈ 174.53 cm^2
I apologize for the mistake in my previous response. You are correct in your calculation.
The total surface area of a closed cylinder with base radius 3 1/3 and height 5cm using the formula 2πr(r+h) is:
2πr(r+h) = 2π(3 1/3)(3 1/3 + 5)
Total surface area = 500/9 π ≈ 174.53 cm²
Thank you for bringing it to my attention.
To calculate the total surface area of a closed cylinder, we need to consider the curved surface area of the side and the two circular bases.
The formula for the surface area of a closed cylinder is:
Surface Area = 2πrh + 2πr^2
where:
- π (pi) is a mathematical constant approximately equal to 3.14159.
- r is the radius of the cylinder's base.
- h is the height of the cylinder.
Given:
- Radius, r = 3 1/3 = 10/3
- Height, h = 5 cm
Now we can substitute these values into the formula and calculate the surface area.
Surface Area = 2π(10/3)(5) + 2π(10/3)^2
= (20/3)π + (200/9)π
To simplify the calculation, let's substitute the value of π as given n = 1/7.
Surface Area = (20/3)(1/7) + (200/9)(1/7)
= 20/21 + 200/63
To add these fractions, we need a common denominator, which is the least common multiple (LCM) of 21 and 63, that is 63. Let's convert the fractions:
Surface Area = (20/21)(3/3) + (200/63)(1/1)
= 60/63 + 200/63
= 260/63
Therefore, the total surface area of the closed cylinder is 260/63 square units.
Total surface area of a closed cylinder = Curved surface area + 2 × Base area
Curved surface area = 2πrh
where r is the base radius and h is the height
Curved surface area = 2π(3\frac{1}{3})(5)
Curved surface area = 106\frac{2}{3}π
Base area = πr^2
Base area = π(3\frac{1}{3})^2
Base area = \frac{34}{3}π
Total surface area = Curved surface area + 2 × Base area
Total surface area = 106\frac{2}{3}π + 2 × \frac{34}{3}π
Total surface area = 106\frac{2}{3}π + \frac{68}{3}π
Total surface area = \frac{320}{3}π
Now, taking n=1/7, we get
Total surface area = \frac{320}{3}π × \frac{1}{7}
Total surface area = \frac{320}{21}π
Therefore, the total surface area of the closed cylinder is \frac{320}{21}π square centimeters.