Mr. Horn purchased a cylindrical aquarium for his office. The aquarium has a height of 25 1/2 inches and a radius of 21 inches. What is the volume of the aquarium in cubic feet?
V = πr^2h
= pi(21^2)(25.5)
=35328.78
To find the volume of the aquarium, we can use the formula for the volume of a cylinder, which is V = πr^2h, where V represents the volume, r represents the radius, and h represents the height.
Given that the radius (r) of the cylindrical aquarium is 21 inches and the height (h) is 25 1/2 inches, we can substitute these values into the formula:
V = π × (21 inches)^2 × (25 1/2 inches)
To convert the measurements from inches to feet, we need to divide each measurement by 12, as there are 12 inches in 1 foot.
Therefore, we have:
V = π × (21 inches ÷ 12 feet)^2 × (25 1/2 inches ÷ 12 feet)
Simplifying further:
V = π × (1.75 feet)^2 × (2.125 feet)
To calculate the square of 1.75, we multiply it by itself:
V = π × 3.0625 square feet × 2.125 feet
Finally, we multiply the two values and multiply by the value of π (approximately 3.14159):
V = 3.14159 × 3.0625 square feet × 2.125 feet
Multiplying these values:
V ≈ 20.32 cubic feet
Therefore, the volume of the cylindrical aquarium is approximately 20.32 cubic feet.
To find the volume of a cylindrical aquarium, we can use the formula:
Volume = π * radius^2 * height
First, let's convert the height and radius to inches. The height is given as 25 1/2 inches, which can be written as a mixed number:
Height = 25 + 1/2 inches
Next, we need to convert the mixed number to an improper fraction:
Height = (25 * 2 + 1) / 2
= 51/2 inches
Now, using the given radius and height, we can calculate the volume:
Volume = π * (21 inches)^2 * (51/2 inches)
To calculate the value of π, we can use an approximation of 3.14159.
Volume ≈ 3.14159 * (21 inches)^2 * (51/2 inches)
Simplifying the calculation:
Volume ≈ 3.14159 * 441 square inches * (51/2 inches)
≈ 3.14159 * 441 * 51 / 2 cubic inches
≈ 34803.726 cubic inches
Finally, we need to convert cubic inches to cubic feet. Since 1 cubic foot is equal to 12^3 = 1728 cubic inches, we can divide the volume by 1728 to get the volume in cubic feet:
Volume in cubic feet = 34803.726 cubic inches / 1728
≈ 20.131 cubic feet
Therefore, the volume of the aquarium is approximately 20.131 cubic feet.