Question

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.

Answer 1

Volume of rectangular prism in scientific notation is
`2.574\cdot10^(6)` cubic centimeters and in standard form
`2574000\text{cm}^(3)`.

Explanation:

Since we know that volume of a rectangular prism is length*breadth*height.

Sides of our rectangular prism are given in scientific notation as
`\text{length}=1.8*10^(2),`
`\text{width}=1.3*10^(2)` and
`\text{height}=1.1*10^(2)`.

Let us substitute our values in volume formula,

`\text{ Volume of rectangular prism}=1.8\cdot 10^(2)\cdot 1.3\cdot 10^(2)\cdot 1.1\cdot 10^(2)`

Upon using exponent product property we will get,

`\text{ Volume of rectangular prism}=1.8\cdot1.3\cdot 1.1\cdot 10^((2+2+2))`

`\text{ Volume of rectangular prism}=2.574\cdot10^(6)\text{cm}^(3)`

Now let us convert our volume in standard form as,

`\text{ Volume of rectangular prism}=2.574\cdot1000000\text{cm}^(3)`

`\text{ Volume of rectangular prism}=2574000\text{cm}^(3)`

Therefore, volume of rectangular prism in scientific notation is
`2.574\cdot10^(6)` cubic centimeters and in standard form
`2574000\text{cm}^(3)`.