Brianna models a can of ground coffee as a right cylinder. She measures its height as
6
1
4
6
4
1
in and its radius as
3
4
4
3
in. Find the volume of the can in cubic inches. Round your answer to the nearest tenth if necessary.
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
Plugging in the given values, we get:
V = π(3/4)²(6 1/4)
Simplifying the radius squared:
V = π(9/16)(25/4)
Multiplying fractions:
V = (225/64)π
Rounding to the nearest tenth:
V ≈ 110.7 cubic inches
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The volume of a right cylinder is given by the formula:
V = πr^2h
where:
V is the volume
π is a mathematical constant equal to about 3.14159
r is the radius
h is the height
Given:
r = 3/4 inches
h = 6 1/4 inches
First, let's convert the mixed number height to an improper fraction:
6 1/4 = 25/4
Now, we can substitute the values into the formula:
V = π(3/4)^2 * (25/4)
V = π(9/16) * (25/4)
V = (9π/16) * (25/4)
Now, let's simplify the expression:
V = (9π * 25)/(16 * 4)
V = (9 * 25 * π) / 64
Using a calculator, let's calculate the approximate value of π:
π ≈ 3.14159
V ≈ (9 * 25 * 3.14159) / 64
V ≈ 706.8582 / 64
V ≈ 11.04003 cubic inches
Therefore, the volume of the can is approximately 11.0 cubic inches.
To find the volume of the can, we can use the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height.
First, let's find the values for r and h:
The radius (r) is given as 3/4.
The height (h) is given as 614641/4.
Now plug in these values into the volume formula:
V = π(3/4)^2 * 614641/4
Now, simplify the expression:
V = π(9/16) * 614641/4
Next, multiply the fractions:
V = (9π/16) * 614641/4
Now, simplify the expression further:
V = 9π * 614641/(16*4)
V = 9π * 614641/64
Finally, calculate the numerical value of the volume:
V ≈ 3437009.2 cubic inches
Therefore, the volume of the can is approximately 3437009.2 cubic inches.