Question
the image shows a cube with the measurements of 5ft
Find the surface area of the cube in square cm.
(2 points)
Responses
150 cm2
125 cm2
75 cm2
25 cm2
Find the surface area of the cube in square cm.
(2 points)
Responses
150 cm2
125 cm2
75 cm2
25 cm2
Answers
GPT-4o mini
To find the surface area of a cube, you can use the formula:
\[
\text{Surface Area} = 6a^2
\]
where \( a \) is the length of a side of the cube.
First, let's convert the measurement from feet to centimeters. We know that:
1 foot = 30.48 cm
So, if the length of a side of the cube is 5 feet:
\[
5 \text{ ft} = 5 \times 30.48 \text{ cm} = 152.4 \text{ cm}
\]
Now we can calculate the surface area:
\[
\text{Surface Area} = 6a^2 = 6 \times (152.4 \text{ cm})^2
\]
Calculating \( (152.4 \text{ cm})^2 \):
\[
(152.4)^2 = 23224.76 \text{ cm}^2
\]
Now we multiply this by 6:
\[
\text{Surface Area} = 6 \times 23224.76 \text{ cm}^2 = 139348.56 \text{ cm}^2
\]
There seems to be a misunderstanding, as the options provided (150 cm², 125 cm², 75 cm², and 25 cm²) are not close to this result. Therefore, the answer must be interpreted correctly or should relate only to the calculations of small units.
If the required answer is close to the given options, please share that additional context. However, as calculated, the correct surface area of a cube with each side measuring 5 ft is much larger than the provided options.
\[
\text{Surface Area} = 6a^2
\]
where \( a \) is the length of a side of the cube.
First, let's convert the measurement from feet to centimeters. We know that:
1 foot = 30.48 cm
So, if the length of a side of the cube is 5 feet:
\[
5 \text{ ft} = 5 \times 30.48 \text{ cm} = 152.4 \text{ cm}
\]
Now we can calculate the surface area:
\[
\text{Surface Area} = 6a^2 = 6 \times (152.4 \text{ cm})^2
\]
Calculating \( (152.4 \text{ cm})^2 \):
\[
(152.4)^2 = 23224.76 \text{ cm}^2
\]
Now we multiply this by 6:
\[
\text{Surface Area} = 6 \times 23224.76 \text{ cm}^2 = 139348.56 \text{ cm}^2
\]
There seems to be a misunderstanding, as the options provided (150 cm², 125 cm², 75 cm², and 25 cm²) are not close to this result. Therefore, the answer must be interpreted correctly or should relate only to the calculations of small units.
If the required answer is close to the given options, please share that additional context. However, as calculated, the correct surface area of a cube with each side measuring 5 ft is much larger than the provided options.