i have a 36 in. wide by 18 in. length by 20 in high rectangular aquarium that needs to be filled. i have a 12 in high cylindrical bucket with a 12 in diameter to fill the tank. if the aquarium contains 3 in of gravel and the bucket is to be filled to a depth of 11 in, how many buckets of water will it take to fill the aquarium?
Assuming the aquarium is to be filled to the top, 20" high less 3" of gravel,
volume of water V1 = 36*18*17 in^3.
Capacity of each bucket filled to 11" high
V2=π(6)^2*11=396π in^3
Number of buckets required = V1/V2
round to the next higher integer.
I get 9 buckets.
To find out how many buckets of water it will take to fill the aquarium, we need to calculate the volume of both the aquarium and the bucket.
First, let's calculate the volume of the aquarium. The aquarium is a rectangular shape, so its volume can be calculated using the formula:
Volume = length × width × height
Given:
Width = 36 in
Length = 18 in
Height = 20 in
Substituting the values into the formula:
Volume of the aquarium = 36 in × 18 in × 20 in
Now, since the aquarium contains 3 in of gravel, the effective height of the aquarium will be reduced by 3 inches. So the new height of the aquarium becomes:
New height = 20 in - 3 in
Next, let's calculate the volume of the bucket. The bucket is cylindrical in shape, so its volume can be calculated using the formula:
Volume = π × r^2 × h
Given:
Height = 12 in
Diameter = 12 in (which means the radius, r, is half of the diameter)
Radius = Diameter / 2 = 12 in / 2 = 6 in
Substituting the values into the formula:
Volume of the bucket = π × 6 in^2 × 12 in
Now, to determine how many buckets it will take to fill the aquarium, we need to divide the volume of the aquarium by the volume of the bucket:
Number of buckets needed = Volume of the aquarium / Volume of the bucket
So, the final step is to divide the calculated volume of the aquarium by the calculated volume of the bucket.