Question

directions: type the correct answer in each box. use numerals instead of words. kristof bought a new terrarium, shaped like a rectangular prism, for his pet snake. the terrarium has a length of (1.8 \times 10^{2}) cm, a width of (1.3 \times 10^{2}) cm, and a height of (1.1 \times 10^{2}) cm. find the volume of the terrarium in scientific notation and in standard form. answers should not be rounded. the volume of the terrarium written in scientific notation is (a \times 10^{b}) cubic cm, where (a) is (square) and (b) is (square). the volume of the terrarium written in standard form is (square) cubic cm.

Explanation:

Step1: Recall volume formula for prism

Volume $V = l \times w \times h$, where $l$=length, $w$=width, $h$=height

Step2: Substitute given values

$V = (1.8 \times 10^2) \times (1.3 \times 10^2) \times (1.1 \times 10^2)$

Step3: Multiply coefficients first

$1.8 \times 1.3 \times 1.1 = 2.574$

Step4: Multiply power-of-10 terms

$10^2 \times 10^2 \times 10^2 = 10^{2+2+2} = 10^6$

Step5: Combine for scientific notation

$V = 2.574 \times 10^6$

Step6: Convert to standard form

$2.574 \times 10^6 = 2574000$

Answer:

The volume of the terrarium written in scientific notation is $a \times 10^b$ cubic cm, where $a$ is $\boldsymbol{2.574}$ and $b$ is $\boldsymbol{6}$.
The volume of the terrarium written in standard form is $\boldsymbol{2574000}$ cubic cm.