Final answer:
The volume of the rectangular prism is 1/8 cubic meters. The volume of a single block with sides of 1/4 meter is 1/64 cubic meters. Since there are eight blocks to fill the rectangular prism, the total volume of the prism is 1/8 cubic meters.
Step-by-step explanation:
To find the volume of the rectangular prism, we need to multiply the lengths of its sides. Since it takes 8 blocks with side lengths of 1/4 meter to fill the prism, we can calculate its volume as follows:
Volume of prism = Number of blocks x Volume of each block
Volume of prism = 8 x (1/4)^3 cubic meters = 8 x 1/64 cubic meters = 1/8 cubic meters
The volume of a single block with sides of 1/4 meter is 1/64 cubic meters. Since there are eight blocks to fill the rectangular prism, the total volume of the prism is 1/8 cubic meters.
The question is asking for the volume of a rectangular prism that is completely filled using 8 blocks, each with side lengths of 1/4 meter. To find the volume of the entire prism, we need to calculate the volume of one block and then multiply it by the number of blocks.
To calculate the volume of one block with side lengths of 1/4 meter, we use the formula for the volume of a cube, which is side length cubed (V = s³). As such, the volume of one block is (1/4 meter) x (1/4 meter) x (1/4 meter) = 1/64 cubic meters. Therefore, the volume of 8 such blocks would be 8 times this amount, which equals 1/8 cubic meters. Thus, the correct answer is 1/8 cubic meters.