Using the correct number of significant figures, calculate the perimeter and volume of a small, rectangular mirror that is 4.040 in long, 1.707 in wide, and 0.078 in thick. Make sure to calculate the the perimeter of the front of the mirror, and not the side. Dimensions are given in inches but the final answer should be in centimeter
Perimeter = 2(4.04) + 2(1.707)
Volume = 4.04 * 1.707 * .078
Convert to cm.
1 inch = 2.54 cm
Sure, let's calculate the perimeter and volume of the mirror!
First, let's convert the dimensions from inches to centimeters:
Length: 4.040 in = 10.26 cm (converted to 4 significant figures)
Width: 1.707 in = 4.34 cm (converted to 4 significant figures)
Thickness: 0.078 in = 0.20 cm (converted to 2 significant figures)
Now let's calculate the perimeter of the front of the mirror (using the length and width):
Perimeter = 2 × (Length + Width)
Perimeter = 2 × (10.26 cm + 4.34 cm)
Perimeter = 2 × 14.60 cm
Perimeter = 29.20 cm (rounded to 4 significant figures)
Next, let's calculate the volume of the mirror (using the length, width, and thickness):
Volume = Length × Width × Thickness
Volume = 10.26 cm × 4.34 cm × 0.20 cm
Volume = 8.89268 cm³ (rounded to 5 significant figures)
So, the perimeter of the front of the mirror is 29.20 cm, and the volume of the mirror is 8.89268 cm³.
To calculate the perimeter of the front of the mirror, we add up the lengths of all four sides. The length (l) and width (w) of the mirror are given as 4.040 in and 1.707 in, respectively.
Perimeter = 2(l + w)
Perimeter = 2(4.040 in + 1.707 in)
Perimeter = 2(5.747 in)
Perimeter = 11.494 in
To convert the answer to centimeters, we use the conversion factor 1 in = 2.54 cm.
Perimeter = 11.494 in * (2.54 cm/1 in)
Perimeter = 29.202 cm
Rounded to the correct number of significant figures, the perimeter of the front of the mirror is 29.2 cm.
To calculate the volume of the mirror, we multiply the length (l), width (w), and thickness (t) together.
Volume = l * w * t
Volume = 4.040 in * 1.707 in * 0.078 in
Volume = 0.543 in³
To convert the answer to centimeters, we use the conversion factor 1 in³ = 16.387 cm³.
Volume = 0.543 in³ * (16.387 cm³/1 in³)
Volume = 8.912 cm³
Rounded to the correct number of significant figures, the volume of the mirror is 8.91 cm³.
To calculate the perimeter of the front of the mirror, we need to add up the lengths of all the sides. The mirror is rectangular, so it has two sides of length 4.040 in, two sides of length 1.707 in, and two sides of thickness 0.078 in.
To calculate the perimeter, we add up all the lengths of the sides:
Perimeter = 2(4.040 in) + 2(1.707 in) + 2(0.078 in)
Now, let's convert the answer to centimeters:
1 in = 2.54 cm, so to convert inches to centimeters, we multiply by 2.54 cm/in.
Perimeter = [2(4.040 in) + 2(1.707 in) + 2(0.078 in)] × 2.54 cm/in
Performing the calculations:
Perimeter = [(2 × 4.040) + (2 × 1.707) + (2 × 0.078)] × 2.54 cm/in
Perimeter = (8.080 + 3.414 + 0.156) × 2.54 cm
Perimeter = 11.650 × 2.54 cm
Perimeter = 29.565 cm
Now, let's calculate the volume of the mirror. The volume of a rectangular prism is given by the formula:
Volume = length × width × thickness.
Volume = 4.040 in × 1.707 in × 0.078 in
Now, convert the answer to centimeters:
Volume = (4.040 in × 1.707 in × 0.078 in) × (2.54 cm/in)³
Performing the calculations:
Volume = (4.040 × 1.707 × 0.078) × (2.54 cm)³
Volume = 0.531 × 4.205 × 0.198 × (2.54 cm)³
Volume = 215.194 cm³
So, the perimeter of the front of the mirror is 29.565 cm (rounded to the correct number of significant figures), and the volume of the mirror is 215.194 cm³ (again, rounded to the correct number of significant figures).
volume in inches: 4.04 * 1.707 * 0.078 = 0.53790984 in.
perimiter in inches: 2 (4.04) + 2 (1.707) = 11.494 in.
vol. in cm. : 1.3662909936
per. in cm. : 29.19476