Question

Taylor is gift wrapping a hat box. Determine the surface area using the net of the hatbox at right. the image shown has a cylinder with a diameter of 30cm and a radius of 10cm.
Use 3.14 for pi (𝜋).


2,512 cm2
2,512 cm2

628 cm2
628 cm2

1884 cm2
1884 cm2

896 cm2

Answer 1

To calculate the surface area of the hat box, which consists of a cylinder and two circular bases, we can use the following formulas:

1. **Lateral Surface Area of the Cylinder** = \( 2 \pi r h \)
2. **Area of the Circular Bases** = \( 2 \times \pi r^2 \)
3. **Total Surface Area** = Lateral Surface Area + Area of the Circular Bases

Given:
- Diameter of the cylinder = 30 cm
- Radius (r) = 30 cm / 2 = 10 cm
- Height (h) needs to be provided or assumed. If not specified, we could assume a height for calculation.

If we assume **h = 20 cm** as an example for calculation:

1. **Lateral Surface Area**:
\[
2 \pi r h = 2 \times 3.14 \times 10 \times 20 = 1256 \text{ cm}^2
\]

2. **Area of the Circular Bases**:
\[
2 \times \pi r^2 = 2 \times 3.14 \times 10^2 = 2 \times 3.14 \times 100 = 628 \text{ cm}^2
\]

3. **Total Surface Area**:
\[
\text{Total Surface Area} = Lateral Surface Area + Area of the Circular Bases
\]
\[
= 1256 + 628 = 1884 \text{ cm}^2
\]

So the surface area of the hat box is **1884 cm²**.

Thus, the answer is: **1884 cm²**.