Kori is calculating the surface area of a cylinder by decomposing it into circles and rectangles. Drag the tiles to match each face of the cylinder with its corresponding area and the cylinder with its surface area.

Question

(The image is a diagram that features a circle with a diameter of 12 inches and additional dimensions of 8 inches. The content appears to be a visual representation, possibly indicating measurements or aspects related to the design. The tags suggest it pertains to diagrams, text, and design elements.)
16π in^2 81π in^2 8π in^2 96π in^2 192π in^2 128π in^2 224π in^2 208π in^2 273π in^2

Answer 1

To calculate the surface area of a cylinder, you will need to consider both the area of the circular bases and the lateral surface area of the cylinder.

1. Given dimensions:

   • Diameter of the base = 12 inches
   • Therefore, the radius \( r = \frac{12}{2} = 6 \) inches.
   • Height \( h = 8 \) inches.

2. Area of the circular bases:

   • The area \( A \) of one circular base is calculated using the formula: \[ A = \pi r^2 \]
   • For the two circular bases, the total area is: \[ A_{\text{bases}} = 2 \pi r^2 = 2 \pi (6^2) = 2 \pi (36) = 72\pi \text{ in}^2 \]

3. Lateral surface area:

   • The lateral surface area \( A_{\text{lateral}} \) is calculated using the formula: \[ A_{\text{lateral}} = 2 \pi r h \]
   • Plugging in the values, \[ A_{\text{lateral}} = 2 \pi (6)(8) = 96\pi \text{ in}^2 \]

4. Total surface area:

   • The total surface area \( A_{\text{total}} \) of the cylinder is the sum of the area of the bases and the lateral area: \[ A_{\text{total}} = A_{\text{bases}} + A_{\text{lateral}} = 72\pi + 96\pi = 168\pi \text{ in}^2 \]

Now, let's look at your tile options:

• We calculated 72π in² for the bases, 96π in² for the lateral area, and the total surface area was 168π in², but this exact value was not provided.

Given the calculated areas:

• Area of one base: \( 36\pi \text{ in}^2 \) (but this was combined for both bases)
• Lateral Area: \( 96\pi \text{ in}^2 \)
• Total Surface Area: Should be \( 168\pi \text{ in}^2 \) (but this is not in the options provided)

Here are suggestions for how to align them based on the options you provided:

• Circle Area (one base): 36π in² (not in options), or if only combined, 72π (matches base areas).
• Lateral Area: 96π in²
• Cylinder Surface Area (close match): If base area additions or other provided values closely fit but given options do not fit the computed total; please review.

However, based solely on provided values:

• For each face:
  • Circle (base): 72π in²
  • Lateral surface: 96π in²

The total computed radius values might yield some error. Could recheck other values available to match fits. If only surface areas needed, likely correctly with given tiles available.