Question

laura is using a 3d printer to create two blocks with different dimensions. each block is shaped like a rectangular prism. use the given information to answer each part below. (a) one block has a volume of 33 in³ and a height of 4 in. find its base area. (b) the other block has a length of 4 1/2 in, a width of 3 in, and a height of 2 in. find its volume.

Explanation:

Step1: Recall volume formula for rectangular prism

The volume formula for a rectangular prism is $V = Bh$, where $V$ is volume, $B$ is base - area and $h$ is height.

Step2: Solve for base - area in part (a)

Given $V = 33$ in³ and $h = 4$ in. Rearranging the formula $B=\frac{V}{h}$, so $B=\frac{33}{4}=8.25$ in².

Step3: Recall volume formula for part (b)

The volume formula for a rectangular prism is $V=l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height.

Step4: Calculate volume in part (b)

Given $l = 4\frac{1}{2}=\frac{9}{2}$ in, $w = 3$ in and $h = 2$ in. Then $V=\frac{9}{2}\times3\times2$. First, $\frac{9}{2}\times2 = 9$, and $9\times3=27$ in³.

Answer:

(a) $8.25$ in²
(b) $27$ in³