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 1.8×10² cm, a width of 1.3×10² cm, and a height of 1.1×10² 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×10ᵇ cubic cm, where a is and b is . the volume of the terrarium written in standard form is cubic cm.

Explanation:

Step1: Recall volume formula for rectangular prism

$V = l\times w\times h$, where $l = 1.8\times10^{2}$, $w = 1.3\times 10^{2}$, $h=1.1\times 10^{2}$.

Step2: Multiply the coefficients

$1.8\times1.3\times1.1=(1.8\times1.3)\times1.1 = 2.34\times1.1=2.574$.

Step3: Multiply the powers of 10

$10^{2}\times10^{2}\times10^{2}=10^{2 + 2+2}=10^{6}$ according to the rule $a^{m}\times a^{n}=a^{m + n}$.

Step4: Write the volume in scientific - notation

$V = 2.574\times10^{6}$ cubic cm. So $a = 2.574$ and $b = 6$.

Step5: Write the volume in standard form

$2.574\times10^{6}=2574000$ cubic cm.

Answer:

The volume of the terrarium written in scientific notation: $a = 2.574$, $b = 6$.
The volume of the terrarium written in standard form: $2574000$