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Riya is applying mulch to her garden. She applies it at a rate of
250,000cm^(3) of mulch for every
m^(2) of garden space.
At what rate is Riya applying mulch in
(m^(3))/(m^(2)) ?

(m^(3))/(m^(2))

Riya is applying mulch to her garden. She applies it at a rate of $250,000\text{cm}^{3}$ of mulch for every $\text{m}^{2}$ of garden space. $\newline$ At what rate is Riya applying mulch in $\left(\frac{\text{m}^{3}}{\text{m}^{2}}\right)$ ?

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Convert rates and measurements: customary units

Full solution

Q. Riya is applying mulch to her garden. She applies it at a rate of

250,000\text{cm}^{3}

of mulch for every

\text{m}^{2}

of garden space.

\newline

At what rate is Riya applying mulch in

\left(\frac{\text{m}^{3}}{\text{m}^{2}}\right)

?

Convert to Cubic Meters: We need to convert the volume of mulch from cubic centimeters to cubic meters. There are $100$ centimeters in a meter, so there are $100^3$ or $1,000,000$ cubic centimeters in a cubic meter.
Divide by Conversion Factor: Now we divide the given volume of mulch in cubic centimeters by the number of cubic centimeters in a cubic meter to convert it to cubic meters. $\newline$ $250,000 \text{ cm}^3 \div 1,000,000 \text{ cm}^3/\text{m}^3 = 0.25 \text{ m}^3$
Rate in Cubic Meters per Square Meter: Since the mulch is applied at a rate per square meter of garden space, the rate in cubic meters per square meter is simply the volume in cubic meters. $\newline$ Therefore, the rate is $0.25 \, \text{m}^3$ of mulch for every $\text{m}^2$ of garden space.

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