Find the volume of the right rectangular prism packed with 12 cubes. Each cube has an edge length of 1/2 inch. (1 point) Responses 5 cubic inches 5 cubic inches 12 cubic inches 12 cubic inches 32 cubic inches Start Fraction 3 over 2 End Fraction cubic inches 18 cubic inches
Use the image to answer the question. How many 1/3 -inch cubes would fit inside the right rectangular prism? (1 point) Responses 48 cubes 48 cubes 12 cubes 12 cubes 24 cubes 24 cubes 7 cubes
18 cubic inches
Each cube has a volume of (1/2)^3 = 1/8 cubic inches. So, the volume of 12 cubes is 12 * (1/8) = 12/8 = 1.5 cubic inches.
Since the prism is packed with 12 cubes, the volume of the prism is 1.5 cubic inches.
To find how many 1/3-inch cubes can fit inside the right rectangular prism, we need to calculate the volume of the rectangular prism and then divide it by the volume of each 1/3-inch cube.
The volume of the right rectangular prism is given by length x width x height = 3(1/3) x 4(1/3) x 2(1/3) = 1 x 4/3 x 2/3 = 8/9 cubic inches.
The volume of each 1/3-inch cube is (1/3)^3 = 1/27 cubic inches.
To find the number of cubes that can fit inside, we divide the volume of the right rectangular prism by the volume of each cube:
(8/9) / (1/27) = (8/9) * (27/1) = 216/9 = 24 cubes.
Therefore, 24 cubes measuring 1/3 inch each can fit inside the right rectangular prism. The correct response is:
24 cubes
What is the volume of the right rectangular prism packed with 8 cubes? Each cube has an edge length of 1/5 centimeter. (1 point) Responses 1125 cubic centimeters Start Fraction 1 over 125 End Fraction cubic centimeters 85 cubic centimeters Start Fraction 8 over 5 End Fraction cubic centimeters 8125 cubic centimeters Start Fraction 8 over 125 End Fraction cubic centimeters 8 cubes
The volume of each cube with an edge length of 1/5 centimeter is (1/5)^3 = 1/125 cubic centimeters.
The volume of 8 cubes would be 8 * (1/125) = 8/125 cubic centimeters.
Therefore, the correct response is:
8/125 cubic centimeters