Question

elijah bought earrings to give to his mother for her birthday. the earrings are in a case shaped like a rectangular prism that is 2 inches long, 1\frac{1}{2} inches wide, and 1\frac{1}{2} inches tall. he doesnt want his mother to guess what the gift is, so he put the case in a larger, cube - shaped gift box. the gift box is 4 inches along each edge. what is the volume of the extra space left in the gift box? cubic inches

Explanation:

Step1: Calculate volume of cube - shaped gift box

The volume formula for a cube is $V = s^3$, where $s$ is the side - length. Here, $s = 4$ inches. So, $V_{box}=4^3=64$ cubic inches.

Step2: Calculate volume of rectangular - prism case

The volume formula for a rectangular prism is $V=l\times w\times h$. Here, $l = 2$ inches, $w = 1\frac{1}{2}=\frac{3}{2}$ inches, and $h = 1\frac{1}{2}=\frac{3}{2}$ inches. So, $V_{case}=2\times\frac{3}{2}\times\frac{3}{2}=\frac{9}{2}=4.5$ cubic inches.

Step3: Calculate extra space volume

The extra space volume $V_{extra}=V_{box}-V_{case}$. Substitute the values: $V_{extra}=64 - 4.5=59.5$ cubic inches.

Answer:

$59.5$