A male moose is 2.6 m tall and 3.2 m long, with antlers that are 1.2 m across.
An artist wants to carve scale models of the moose. She uses a scale factor of 1/30.
a) What are the dimensions of the carvings to the nearest centimetre?
b) How many carvings can she make using part of a railway tie that is 22 cm by 18 cm by 32 cm?
change your m to cm (real easy, just multiply by 100), then divide each of those by 30 to get
8.67 by 10.67 by 4
so she must start with a block of that size
32÷(32/3) =3 --- 3 lengths
22÷(26/3) = 2.5 --- not enough for 3 heights
looks like she can only make 2 carvings
To find the dimensions of the carvings, we can use the scale factor of 1/30 and multiply it by the dimensions of the real moose.
a) Dimensions of the carvings:
Height: 2.6 m x 1/30 = 0.0867 m or 8.67 cm (to the nearest centimetre)
Length: 3.2 m x 1/30 = 0.1067 m or 10.67 cm (to the nearest centimetre)
Antler width: 1.2 m x 1/30 = 0.04 m or 4 cm (to the nearest centimetre)
Therefore, the dimensions of the carvings are approximately 8.67 cm in height, 10.67 cm in length, and 4 cm in antler width.
b) To find out how many carvings can be made using the given part of a railway tie, we need to calculate the maximum number of carvings that can fit within the dimensions of the tie.
The dimensions of the tie are:
Length: 22 cm
Width: 18 cm
Height: 32 cm
To calculate the number of carvings, we need to divide the available dimensions of the tie by the dimensions of the carvings:
Number of Carvings = (Length of Tie / Length of Carving) * (Width of Tie / Width of Carving) * (Height of Tie / Height of Carving)
Number of Carvings = (22 cm / 10.67 cm) * (18 cm / 4 cm) * (32 cm / 8.67 cm)
Number of Carvings = 2.063 * 4.5 * 3.688
Number of Carvings = 34.5288
Therefore, the artist can make approximately 34 carvings using the part of the railway tie.
To find the dimensions of the carvings, we need to apply the scale factor of 1/30 to the dimensions of the male moose.
a) Dimensions of the carvings:
Height: 2.6 m * (1/30) = 0.0866667 m
Length: 3.2 m * (1/30) = 0.1066667 m
Antler Width: 1.2 m * (1/30) = 0.04 m
To convert these dimensions to centimeters, we multiply by 100:
Height: 0.0866667 m * 100 = 8.67 cm (rounded to the nearest centimeter)
Length: 0.1066667 m * 100 = 10.67 cm (rounded to the nearest centimeter)
Antler Width: 0.04 m * 100 = 4 cm
Therefore, the dimensions of the carvings to the nearest centimeter are approximately 8.67 cm (height), 10.67 cm (length), and 4 cm (antler width).
b) To calculate how many carvings can be made using the railway tie, we need to divide the volume of the railway tie by the volume of a single carving.
Volume of the railway tie:
Volume = Length * Width * Height
Volume = 22 cm * 18 cm * 32 cm = 12672 cm³
Volume of a single carving:
Volume = Height * Length * Antler Width
Volume = 8.67 cm * 10.67 cm * 4 cm = 368.19 cm³ (rounded to two decimal places)
Now, we can find the number of carvings by dividing the volume of the railway tie by the volume of a single carving:
Number of carvings = Volume of railway tie / Volume of single carving
Number of carvings = 12672 cm³ / 368.19 cm³ = 34.42 (rounded to two decimal places)
Therefore, the artist can make approximately 34 carvings using part of a railway tie that is 22 cm by 18 cm by 32 cm.