Question

If a box has a length of 10.0 cm, a width of 15 cm, and a height of 5.0 cm, then what is its volume in m3 ?

Responses

7.5×10−4

7.5 times 10 to the power of negative 4

7.5×102

7.5 times 10 squared

7.5×10−3

7.5 times 10 to the power of negative 3

750×102

Answer 1

7.5 × 10⁻⁴

Step-by-step explanation:

`\boxed{\begin{minipage}{5cm}\underline{Volume of a rectangular prism}\\\\\sf V = Length $*$ Width $*$ Height\\\end{minipage}}`

The box can be modeled as a rectangular prism with:

• Length = 10 cm
• Width = 15 cm
• Height = 5 cm

Substitute the given dimensions into the formula to find the volume of the box in cm³:

`\begin{aligned}\implies \sf Volume&=\sf Length * Width * Height\\& = \sf 10 * 15 * 5\\& = \sf 150 times 5\\& = \sf 750 \; cm^3\end{aligned}`

As 100 cm = 1 m :

⇒ (100 cm)³ = (1 m)³

⇒ 1,000,000 cm³ = 1 m³

Therefore, to convert the volume of the box into cubic meters, divide the volume in cubic centimeters by 1,000,000.

`\begin{aligned}\implies (750)/(1000000)&=(7.5 * 10^2)/(1.0 * 10^6)\\&=(7.5)/(1.0) * (10^2)/(10^6)\\&=7.5 * 10^((2-6))\\&=7.5 * 10^(-4)\end{aligned}`

Therefore, the volume of the box is 7.5 × 10⁻⁴ m³.