Question

Keith 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 36 cubed and a height of 5. Find its base area.

(b)The other block has a length of 4 1/2, a width of3 , and a height of 2. Find its volume.

Answer 1

To solve the problem, we'll use the formulas for the volume and base area of a rectangular prism.

### (a) Finding the base area of the first block

We know the formula for the volume \( V \) of a rectangular prism is given by:

\[
V = \text{base area} \times \text{height}
\]

Given that the volume \( V \) is 36 cubic units and the height \( h \) is 5 units, we can rearrange the formula to find the base area \( A \):

\[
A = \frac{V}{h}
\]

Substituting the given values:

\[
A = \frac{36}{5} = 7.2 \text{ square units}
\]

So, the base area of the first block is \( 7.2 \) square units.

### (b) Finding the volume of the second block

For the second block, we have the length \( l = 4.5 \), width \( w = 3 \), and height \( h = 2 \). The volume \( V \) can be calculated using the formula:

\[
V = l \times w \times h
\]

Substituting the given dimensions:

\[
V = 4.5 \times 3 \times 2
\]

Calculating step by step:

1. Calculate \( 4.5 \times 3 = 13.5 \).
2. Now calculate \( 13.5 \times 2 = 27 \).

Thus, the volume of the second block is \( 27 \) cubic units.

### Final Answers
(a) The base area of the first block is \( 7.2 \) square units.
(b) The volume of the second block is \( 27 \) cubic units.