The new shark tank at the city aquarium is in the shape of a rectangular prism. It is 78ft long by  39ft wide by 18ft deep. To make the tank livable for the sharks, the aquarium workers treat the water using bags of salt. The amount of water a bag of salt can treat is known in cubic yards.
(a)	Find the volume of water in the tank in cubic yards. Use the table of conversion facts, as needed.

(b)	To make the tank livable for the sharks, a bag of salt must be added for each 1.8yd(3) of water. The aquarium doesn't have any salt on hand and the salt can only be purchased in whole bags. How many bags of salt must be purchased to treat the water?

(c)	If each bag of salt costs $5.10 , how much must the aquarium pay for salt to treat all the water in the new shark tank?

We can solve this step by step. Let's break it down:

### (a) Find the volume of water in the tank in cubic yards.

The tank is shaped like a rectangular prism, so the volume $ V $ of the tank is given by the formula for the volume of a rectangular prism:

\[
V = \text{length} \times \text{width} \times \text{depth}
\]

The dimensions of the tank are given in feet:

- Length = 78 ft
- Width = 39 ft
- Depth = 18 ft

The volume will first be calculated in cubic feet. Then, we'll convert the volume from cubic feet to cubic yards, using the conversion factor: 
\[
1 \text{ yard} = 3 \text{ feet} \quad \text{so} \quad 1 \text{ cubic yard} = 3^3 = 27 \text{ cubic feet}.
\]

Now let's calculate:

1. Calculate the volume in cubic feet:
\[
V_{\text{cubic feet}} = 78 \times 39 \times 18
\]

2. Convert this volume to cubic yards by dividing the result by 27:
\[
V_{\text{cubic yards}} = \frac{V_{\text{cubic feet}}}{27}
\]

### (b) How many bags of salt must be purchased?

We are told that each bag of salt treats 1.8 cubic yards of water, and we can only purchase whole bags. Therefore, the total number of bags of salt $ N $ required is:

\[
N = \frac{\text{Volume in cubic yards}}{1.8}
\]

We will round up to the next whole number, since any partial bag cannot be used.

### (c) Calculate the cost of the salt.

Each bag of salt costs \$5.10. To find the total cost, multiply the number of bags by the price per bag:

\[
\text{Total cost} = N \times 5.10
\]

Let's calculate these results.### (a) The volume of the water in the tank is 2,028 cubic yards.

### (b) To treat the water, the aquarium must purchase 1,127 bags of salt.

### (c) The total cost to purchase the salt is \$5,747.70.

Would you like more details or have any questions?

Here are five related questions to explore:

1. What is the volume of the tank in gallons of water?
2. How many cubic meters of water does the tank hold?
3. What happens to the volume calculation if the tank has a sloped bottom instead of a flat one?
4. How much would it cost if each bag of salt treated 2.0 cubic yards instead of 1.8?
5. What would the cost be if the price per bag increased by 10%?

**Tip:** Always check whether rounding is needed when dealing with quantities like bags of salt or people!

The new shark tank at the city aquarium is in the shape of a rectangular prism. It is 78ft long by 39ft wide by 18ft deep. To make the tank livable for the sharks, the aquarium workers treat the water using bags of salt. The amount of water a bag of salt can treat is known in cubic yards.
(a) Find the volume of water in the tank in cubic yards. Use the table of conversion facts, as needed.
(b) To make the tank livable for the sharks, a bag of salt must be added for each 1.8yd(3) of water. The aquarium doesn't have any salt on hand and the salt can only be purchased in whole bags. How many bags of salt must be purchased to treat the water?
(c) If each bag of salt costs $5.10, how much must the aquarium pay for salt to treat all the water in the new shark tank?

Learn how to calculate the volume of water in a shark tank (78ft by 39ft by 18ft) in cubic yards, how many bags of salt are needed to treat the water, and the total cost for the aquarium. This problem uses key concepts such as volume calculation, unit conversion, and cost estimation. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation