Question

The base of the tank (10.5x7.5x7.5) needs to have 3 cm deep gravel. Gravel costs $5 for 500g bags from the pet store.
Calculate the volume of gravel required to cover the base on your tank to a depth of 3 cm.
If gravel has a density of 2.5 g/cm3, calculate the weight of gravel
Now calculate the cost of gravel needed.

Answer 1

Answer on Question #82499 – Math – Algebra

Question

The base of the tank (10.5x7.5x7.5) needs to have 3 cm deep gravel. Gravel costs $5 for 500g bags from the pet store. Calculate the volume of gravel required to cover the base on your tank to a depth of 3 cm. If gravel has a density of 2.5 g/cm³, calculate the weight of gravel. Now calculate the cost of gravel needed.

Solution

We will calculate gravel volume necessary for a tank basis covering to a depth of 3 cm.

$$V = 10.5 \times 7.5 \times 3 = 236.25 \text{cm}^3$$

Find the mass of gravel using formula

$$m = \rho V = 2.5 \frac{g}{\text{cm}^3} \times 236.25 \text{cm}^3 = 590.625g$$

Hence the cost of gravel is equal to

$$c = \frac{590.625}{500} \cdot 5\% \approx 5.91\%$$

Answer. $V = 236.25 \text{cm}^3$; $m = 590.625g$; c = 5.91\

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