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:
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Volume of a Cylinder: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.
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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: \( 471 , \text{mm}^2 \)