20 cm

Question

- 27 cm • Front
A box needs to be decorated to use as a prop in a play. The bottom and the back of the box do not need to be decorated.
What is the surface area of the box that needs to be decorated?
(1 point)
• 1, 880 cm₴
• 67 cm?
• 1,080 cm
O 2, 960 cm?

Answer 1

To find the surface area of the box that needs to be decorated, we'll first need to establish the dimensions of the box. From the information provided, we know two dimensions:

• Height = 20 cm
• Depth (width) = 27 cm
• We will need the width (depth) to complete the surface area calculation. Let's denote the width of the box as \( w \).

Assuming the box has a width (let's call it \( w \)), the relevant faces that need decoration are:

1. The front side (which would be \( height \times width \))
2. The two side walls (each side wall has an area of \( height \times depth \))
3. The top (which has an area of \( width \times depth \))

The areas we need to calculate are:

1. Front area: \( A_{front} = height \times width = 20 , \text{cm} \times w \)
2. Two side walls: \( A_{side} = 2 \times (height \times depth) = 2 \times (20 , \text{cm} \times 27 , \text{cm}) \)
3. Top area: \( A_{top} = width \times depth = w \times 27 , \text{cm} \)

So the total surface area that needs to be decorated is:

\[ A_{total} = A_{front} + A_{side} + A_{top} \] \[ = (20w) + 2(20 \cdot 27) + (w \cdot 27) \] \[ = 20w + 1080 + 27w \] \[ = 47w + 1080 \]

To find the specific area that needs to be decorated, we would need to know the width (\( w \)). If the options for the surface area provided are:

1. 1,880 cm²
2. 67 cm²
3. 1,080 cm²
4. 2,960 cm²

From the calculated total surface area, we can see that \( 1,080 , \text{cm}^2 \) corresponds to when \( w = 0 \) (just the side areas), and as \( w \) increases, the total surface area will increase. The closest value seems to be \( 1,880 , \text{cm}^2 \) or more based on simple assumptions about reasonable widths (e.g., assuming \( w \) is around 17 cm), leading to higher estimates.

Calculating the surface area for practical values of \( w\) would yield:

If \( w = 12 cm \): \[ A_{total} = 47(12) + 1080 = 564 + 1080 = 1644 cm² \]

If \( w = 15 cm \): \[ A_{total} = 47(15) + 1080 = 705 + 1080 = 1785 cm² \]

The exact width would depend on context, but with the above choices, none clearly match without \( w \) being specified.

To choose from provided answers, we suggest re-evaluating in context, knowing those dimension figures. Additional context for width \( w \) is thus necessary, or default to reasonable approximations leading back to summation in available datasets of options across character prop designs.