Bot GPT 4-o mini To find the diagonal \( d \) of a rectangular prism (also known as a box) with dimensions \( a \), \( b \), and \( c \), we use the formula:
\[ d = \sqrt{a^2 + b^2 + c^2} \]
In this case, the dimensions of the box are:
- \( a = 3 \) cm
- \( b = 4 \) cm
- \( c = 10 \) cm
Now, we substitute these values into the formula:
\[ d = \sqrt{3^2 + 4^2 + 10^2} \]
Calculating each term:
\[ 3^2 = 9 \] \[ 4^2 = 16 \] \[ 10^2 = 100 \]
Now, add these values together:
\[ d = \sqrt{9 + 16 + 100} = \sqrt{125} \]
Next, we calculate \( \sqrt{125} \):
\[ \sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5} \]
Using a calculator, \( \sqrt{5} \) is approximately \( 2.236 \), so:
\[ d \approx 5 \times 2.236 \approx 11.18 \]
Rounding to the nearest tenth:
\[ d \approx 11.2 \text{ cm} \]
Thus, the diagonal of the rectangular prism box is approximately \( \boxed{11.2} \) cm.
1 answer