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Find the lateral surface area of a cylinder with a radius of 2.5 meters and a height of 7 meters.

Use 3.14 for pi and round your answer to the nearest tenth.

3 answers

The formula for the lateral surface area \( A \) of a cylinder is given by:

\[ A = 2 \pi r h \]

where:

  • \( r \) is the radius,
  • \( h \) is the height,
  • \( \pi \) is approximately 3.14.

Given:

  • \( r = 2.5 \) meters,
  • \( h = 7 \) meters,
  • \( \pi \approx 3.14 \).

Now, substituting the values into the formula:

\[ A = 2 \times 3.14 \times 2.5 \times 7 \]

Calculating step by step:

  1. Calculate \( 2.5 \times 7 \):

\[ 2.5 \times 7 = 17.5 \]

  1. Now multiply by \( 3.14 \):

\[ 3.14 \times 17.5 = 54.95 \]

  1. Finally, multiply by 2:

\[ A = 2 \times 54.95 = 109.9 \]

So, the lateral surface area of the cylinder is \( 109.9 \) square meters.

Rounded to the nearest tenth, the answer is:

\[ \boxed{109.9} \text{ square meters} \]

What is the total surface area of the cylinder from the last question.
1. 149.5
2. 515.0
3. 129.52
4. 266.9

To find the total surface area \( A_t \) of a cylinder, we use the formula:

\[ A_t = 2\pi r h + 2\pi r^2 \]

This formula includes the lateral surface area (which we calculated previously) and the areas of the two circular bases.

We already know:

  • The lateral surface area \( A_l = 109.9 \) square meters (from the previous calculation).
  • The radius \( r = 2.5 \) meters.
  • The height \( h = 7 \) meters.
  • We will continue using \( \pi \approx 3.14 \).

Now we need to calculate the area of the two circular bases:

  1. Area of one base:

\[ \text{Area of one base} = \pi r^2 = 3.14 \times (2.5)^2 \]

Calculating \( (2.5)^2 \):

\[ (2.5)^2 = 6.25 \]

Now calculating the area of one base:

\[ \text{Area of one base} = 3.14 \times 6.25 = 19.625 \]

  1. Since there are two bases, multiply by 2:

\[ \text{Total area of the bases} = 2 \times 19.625 = 39.25 \]

  1. Now add the lateral surface area and the total area of the bases to find the total surface area:

\[ A_t = A_l + \text{Total area of the bases} = 109.9 + 39.25 = 149.15 \]

Rounding to the nearest tenth, we get \( 149.2 \) square meters.

Comparing this value to the choices given:

  1. 149.5
  2. 515.0
  3. 129.52
  4. 266.9

The closest answer is 149.5.

Thus, the correct answer is:

\[ \boxed{149.5} \]