Question

a cylinder has a radius of 5 mm and a height of 10 mm use 3.14 for pi

Answer 1

To find the volume and surface area of a cylinder with a radius of 5 mm and a height of 10 mm, we can use the following formulas:

1. **Volume of a Cylinder**:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.

2. **Surface Area of a Cylinder**:
\[
A = 2\pi r(h + r)
\]
where \( r \) is the radius and \( h \) is the height.

### Step 1: Calculate the Volume

Using \( r = 5 \, \text{mm} \) and \( h = 10 \, \text{mm} \), and substituting \( \pi = 3.14 \):

\[
V = \pi r^2 h = 3.14 \times (5 \, \text{mm})^2 \times 10 \, \text{mm}
\]
\[
= 3.14 \times 25 \, \text{mm}^2 \times 10 \, \text{mm}
\]
\[
= 3.14 \times 250 \, \text{mm}^3
\]
\[
= 785 \, \text{mm}^3
\]

### Step 2: Calculate the Surface Area

Using the same values for \( r \) and \( h \):

\[
A = 2\pi r(h + r) = 2 \times 3.14 \times 5 \, \text{mm} \times (10 \, \text{mm} + 5 \, \text{mm})
\]
\[
= 2 \times 3.14 \times 5 \, \text{mm} \times 15 \, \text{mm}
\]
\[
= 2 \times 3.14 \times 75 \, \text{mm}^2
\]
\[
= 2 \times 235.5 \, \text{mm}^2
\]
\[
= 471 \, \text{mm}^2
\]

### Summary:

- **Volume**: \( 785 \, \text{mm}^3 \)
- **Surface Area**: \( 471 \, \text{mm}^2 \)