To find out how much fabric Krubell needs to make his pencil case in the shape of a circular cylinder, we'll calculate the surface area of the cylinder. The surface area (SA) of a cylinder can be calculated using the formula:
\[ SA = 2\pi r(h + r) \]
Where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \(\pi\) is approximately 3.14 (or you can use the more precise value of \(\pi \approx 3.14159\)).
Given:
- Radius \( r = 3 \) cm
- Height \( h = 22 \) cm
Let's substitute these values into the formula:
\[ SA = 2 \pi (3)(22 + 3) \] \[ = 2 \pi (3)(25) \] \[ = 6\pi(25) \] \[ = 150\pi \]
Now, using \( \pi \approx 3.14 \):
\[ SA \approx 150 \times 3.14 \approx 471 \text{ cm}^2 \]
So, the surface area of the pencil case (the fabric needed) is approximately 471 cm².
The correct answer is C: 471 cm².