To find out how much fabric Krubell will need to make his cylindrical pencil case, we need to calculate the surface area of the cylinder. The surface area \( A \) of a cylinder is given by the formula:
\[ A = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder, and
- \( \pi \) (pi) is approximately 3.14.
Given:
- radius \( r = 3 , \text{cm} \)
- height \( h = 22 , \text{cm} \)
Let's plug the values into the formula:
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Calculate \( h + r \): \[ h + r = 22 , \text{cm} + 3 , \text{cm} = 25 , \text{cm} \]
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Substitute the values into the surface area formula: \[ A = 2 \times 3.14 \times 3 \times 25 \]
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First, calculate \( 2 \times 3.14 \times 3 \): \[ 2 \times 3.14 = 6.28 \] \[ 6.28 \times 3 = 18.84 \]
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Now multiply by \( 25 \): \[ A = 18.84 \times 25 = 471 \]
So, the total surface area of the pencil case is approximately \( 471 , \text{cm}^2 \).
Therefore, Krubell will need 471 cm² of fabric to make his pencil case.