Question

a right rectangular prism has a base area of $2\frac{1}{2}$ square inches and a height of $11\frac{1}{2}$ inches. what is the volume of the prism? a. $14\\ \text{in}^3$ b. $28\frac{3}{4}\\ \text{in}^3$ c. $71\frac{7}{8}\\ \text{in}^3$ d. $86\frac{1}{4}\\ \text{in}^3$

Explanation:

Step1: Convert mixed numbers to fractions

Base area: $2\frac{1}{2} = \frac{5}{2}$ in², Height: $11\frac{1}{2} = \frac{23}{2}$ in

Step2: Apply volume formula for prism

Volume = Base Area × Height
$\text{Volume} = \frac{5}{2} \times \frac{23}{2}$

Step3: Calculate the product

$\text{Volume} = \frac{5 \times 23}{2 \times 2} = \frac{115}{4}$

Step4: Convert to mixed number

$\frac{115}{4} = 28\frac{3}{4}$ in³

Answer:

B. $28\frac{3}{4}$ in³