Question

(a) one block has a length of 4 1/4 in, a width of 3 in, and a height of 4 in. find its volume. (b) the other block has a volume of 26 1/4 in³ and a base area of 15 in². find its height. base area = 15 in²

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - prism is $V = l\times w\times h$ (or $V=B\times h$, where $B$ is the base - area).

Step2: Calculate volume for part (a)

Given $l = 4\frac{1}{4}$ in, $w = 3$ in, $h = 4$ in. First, convert $4\frac{1}{4}$ to an improper fraction: $4\frac{1}{4}=\frac{4\times4 + 1}{4}=\frac{17}{4}$ in. Then $V=l\times w\times h=\frac{17}{4}\times3\times4$. Using the commutative property of multiplication, $V=\frac{17}{4}\times4\times3$. $\frac{17}{4}\times4 = 17$, and $17\times3=51$ in³.

Step3: Calculate height for part (b)

Given $V = 26\frac{1}{4}$ in³ and $B = 15$ in². Convert $26\frac{1}{4}$ to an improper fraction: $26\frac{1}{4}=\frac{26\times4+1}{4}=\frac{105}{4}$ in³. Since $V = B\times h$, then $h=\frac{V}{B}$. Substitute $V=\frac{105}{4}$ in³ and $B = 15$ in² into the formula: $h=\frac{\frac{105}{4}}{15}=\frac{105}{4}\div15=\frac{105}{4}\times\frac{1}{15}=\frac{105}{60}=\frac{7}{4}=1\frac{3}{4}$ in.

Answer:

(a) $51$ in³
(b) $1\frac{3}{4}$ in