The new shark tank at the city aquarium is in the shape of a rectangular prism. It is
69ft
long by
45ft
wide by
12ft
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.
yd3
(b) To make the tank livable for the sharks, a bag of salt must be added for each
1.3yd3
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?
bags
(c) If each bag of salt costs
$4.65
, how much must the aquarium pay for salt to treat all the water in the new shark tank?
(a) To find the volume of water in cubic yards, we need to convert the dimensions from feet to yards first:
Length: 69ft ÷ 3 = 23yd
Width: 45ft ÷ 3 = 15yd
Depth: 12ft ÷ 3 = 4yd
Then we can calculate the volume:
Volume = Length x Width x Depth = 23yd x 15yd x 4yd = 1380yd³
Therefore, the volume of water in the tank is 1380 cubic yards.
(b) To treat the water, we need to add one bag of salt for every 1.3 cubic yards of water. We can use division to find out how many bags are needed:
Number of bags needed = Volume of water ÷ Volume of water per bag
Number of bags needed = 1380yd³ ÷ 1.3yd³/bag
Number of bags needed = 1061.54 bags
Since we can only purchase whole bags of salt, we need to round up to the nearest whole number. Therefore, we need to purchase 1062 bags of salt.
(c) If each bag of salt costs $4.65, we can multiply the number of bags by the cost per bag to find the total cost:
Total cost = Number of bags x Cost per bag
Total cost = 1062 bags x $4.65/bag
Total cost = $4929.30
Therefore, the aquarium must pay $4929.30 for salt to treat all the water in the new shark tank.
1061.54 as a whole number
1062 (rounded up to the nearest whole number).
(a) To find the volume of water in the tank in cubic yards, we multiply the dimensions of the tank (in feet) together:
Volume = length × width × depth
Volume = 69 ft × 45 ft × 12 ft
Now we convert the volume from cubic feet to cubic yards. There are 27 cubic feet in a cubic yard.
Volume = (69 ft × 45 ft × 12 ft) / 27
Volume ≈ 3456 ft³ / 27 ≈ 128 ft³
So the volume of water in the tank is approximately 128 cubic yards.
(b) To determine the number of bags of salt needed, we divide the volume of water by the volume of water each bag of salt can treat:
Number of bags = Volume of water / Volume treated by each bag
Number of bags = 128 yd³ / 1.3 yd³
Number of bags ≈ 98.46
Since we can only purchase whole bags, we need to round up to the nearest whole number. Therefore, the aquarium needs to purchase 99 bags of salt to treat the water.
(c) If each bag of salt costs $4.65, the total cost for all the salt needed can be calculated by multiplying the number of bags by the cost per bag:
Total cost = Number of bags × Cost per bag
Total cost = 99 bags × $4.65/bag
Total cost ≈ $460.35
Therefore, the aquarium needs to pay approximately $460.35 for salt to treat all the water in the new shark tank.
To solve this problem, we need to find the volume of water in the tank, calculate the number of bags of salt needed to treat the water, and then determine the cost of the salt.
(a) To find the volume of water in the tank in cubic yards, we need to multiply the length, width, and depth of the tank. The volume formula for a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
V = 69 ft * 45 ft * 12 ft
But we need the volume in cubic yards, so we need to convert the feet to yards. Since 1 yard is equal to 3 feet, we divide each dimension by 3.
V = (69 ft / 3 yd) * (45 ft / 3 yd) * (12 ft / 3 yd)
Simplifying, we get:
V = 23 yd * 15 yd * 4 yd
V = 1380 yd³
So, the volume of water in the tank is 1380 cubic yards.
(b) To determine the number of bags of salt needed to treat the water, we divide the volume of water by the amount of water a bag of salt can treat, which is given as 1.3 cubic yards.
Number of bags = 1380 yd³ / 1.3 yd³
Number of bags ≈ 1061 bags
Therefore, 1061 bags of salt must be purchased to treat the water.
(c) To calculate the cost of the salt, we multiply the number of bags by the cost per bag, which is given as $4.65.
Cost of salt = Number of bags * Cost per bag
Cost of salt = 1061 bags * $4.65/bag
Cost of salt ≈ $4935.65
So, the aquarium must pay approximately $4935.65 for the salt to treat all the water in the new shark tank.