The new dolphin tank at the city aquarium is in the shape of a rectangular prism. It is $25 \mathrm{yd}$ long by 14 yd wide by 5 yd deep. To make the tank livable for the dolphins, the aquarium workers treat the water using bags of salt. The amount of water a bag of salt can treat is known in cubic feet.
(a) Find the volume of water in the tank in cubic feet. Use the table of conversion facts, as needed.
(b) To make the tank livable for the dolphins, a bag of salt must be added for each $22.6 \mathrm{ft}^{3}$ of water. The aquarium doesn't have any salt on hand and the sait can only be purchased in whole bags. How many bags of salt must be purchased to treat the water?
bags
(c) If each bag of salt costs $\$ 5.30$, how much must the aquarium pay for salt to treat all the water in the new dolphin tank?
Conversion facts for length
1 foot $(\mathrm{ft})=12$ inches (in)
1 yard $(\mathrm{yd})=3$ feet $(\mathrm{ft})$
1 yard $(y d)=36$ inches $($ in)
Answer
Final Answer: The volume of the water in the tank is \(\boxed{47250.0 ft^3}\). The aquarium should purchase \(\boxed{2091}\) bags of salt.
Step 1 ：Given that the tank is in the shape of a rectangular prism, with a length of \(25 yd\), a width of \(14 yd\), and a depth of \(5 yd\).
Step 2 ：The volume of a rectangular prism is calculated by multiplying its length, width, and height. So, the volume of the water in the tank in cubic yards is \(25 yd * 14 yd * 5 yd = 1750 yd^3\).
Step 3 ：Since 1 yard is equal to 3 feet, we need to convert the volume from cubic yards to cubic feet. We do this by cubing the conversion factor, so \(1 yd^3 = (3 ft)^3 = 27 ft^3\). Therefore, the volume of the tank water in cubic feet is \(1750 yd^3 * 27 = 47250 ft^3\).
Step 4 ：The instructions for the salt say that one bag of salt is needed for every \(22.6 ft^3\) of tank water. So, the number of bags needed is \(\frac{47250 ft^3}{22.6 ft^3/bag} = 2090.27 bags\).
Step 5 ：Since the aquarium can only purchase whole bags of salt, they need to round up to the nearest whole number. Therefore, they need to purchase 2091 bags of salt.
Step 6 ：Final Answer: The volume of the water in the tank is \(\boxed{47250.0 ft^3}\). The aquarium should purchase \(\boxed{2091}\) bags of salt.
