Find the surface area of the cylinder that ahs a diameter of 2 yards and a height of 3 yards sue the aproximation 3.14 as pi

75.26
62.8
25.12
32.97

3 answers

The surface area \( S \) of a cylinder is given by the formula:

\[ S = 2\pi r^2 + 2\pi rh \]

where:

  • \( r \) is the radius of the cylinder,
  • \( h \) is the height of the cylinder.

Given that the diameter of the cylinder is 2 yards, we can find the radius:

\[ r = \frac{\text{diameter}}{2} = \frac{2 \text{ yards}}{2} = 1 \text{ yard} \]

The height \( h \) is given as 3 yards.

Now, we can substitute these values into the surface area formula. Using \( \pi \approx 3.14 \):

  1. Calculate \( 2\pi r^2 \):

\[ 2\pi r^2 = 2 \times 3.14 \times (1)^2 = 2 \times 3.14 \times 1 = 6.28 \]

  1. Calculate \( 2\pi rh \):

\[ 2\pi rh = 2 \times 3.14 \times 1 \times 3 = 2 \times 3.14 \times 3 = 18.84 \]

  1. Now, add both parts together to get the total surface area:

\[ S = 6.28 + 18.84 = 25.12 \]

Thus, the surface area of the cylinder is \( \boxed{25.12} \) square yards.

are you sure

Let's double-check the calculation step by step.

The formula for the surface area of a cylinder is:

\[ S = 2\pi r^2 + 2\pi rh \]

  1. Find the radius: Given that the diameter is 2 yards, the radius \( r \) is: \[ r = \frac{\text{diameter}}{2} = \frac{2 \text{ yards}}{2} = 1 \text{ yard} \]

  2. Given values:

    • Radius \( r = 1 \) yard
    • Height \( h = 3 \) yards
    • Use \( \pi \approx 3.14 \)
  3. Calculate \( 2\pi r^2 \): \[ 2\pi r^2 = 2 \times 3.14 \times (1)^2 = 2 \times 3.14 \times 1 = 6.28 \text{ square yards} \]

  4. Calculate \( 2\pi rh \): \[ 2\pi rh = 2 \times 3.14 \times 1 \times 3 = 2 \times 3.14 \times 3 = 18.84 \text{ square yards} \]

  5. Add the two parts to find the total surface area: \[ S = 6.28 + 18.84 = 25.12 \text{ square yards} \]

Yes, the calculation holds true, and the surface area of the cylinder is indeed \( \boxed{25.12} \) square yards.