A cylindrical beaker has a height of 5 inches and a volume of 63 cubic inches. A scientist pours a chemical from the beaker to a similar beaker with a height that is 100% greater.
What is the volume of the larger beaker?
The volume of the larger beaker would be 504 inches cubed.
I should clarify how to solve the problem. We start with V = pi r^2 h.
Solve for r^2; 63 = pi r^2 5. First divide by pi and then by 5. Get the square root of your answer (4.0107) to get the radius of 2.002674. Next we increase everything by 100% and use a height of 10 and a radius of 4.005348. Using the equation above and you will get the volume of 503.9998 or 504.
To find the volume of the larger beaker, we need to determine the height of the larger beaker first.
Given that the height of the original beaker is 5 inches, and the height of the larger beaker is 100% greater, we can calculate the height of the larger beaker by adding 100% of the original height to the original height.
100% of 5 inches is (100/100) * 5 = 5 inches.
Adding 5 inches to the original height of 5 inches gives us the height of the larger beaker, which is 5 + 5 = 10 inches.
Now, since the larger beaker is similar to the original beaker, it means their dimensions are proportional.
The ratio of the heights of the two beakers is 10 inches (larger beaker) to 5 inches (original beaker), which simplifies to 2:1.
Since the dimensions are proportional, the ratio of their volumes will be equal to the cube of the ratio of their heights.
The cube of the ratio is 2^3 : 1^3 = 8 : 1.
Given that the volume of the original beaker is 63 cubic inches, we can find the volume of the larger beaker by multiplying the volume of the original beaker by the ratio.
63 cubic inches multiplied by 8/1 equals 63 * 8 = 504 cubic inches.
Therefore, the volume of the larger beaker is 504 cubic inches.
To find the volume of the larger beaker, we need to first determine the height of the larger beaker.
The height of the larger beaker is 100% greater than the height of the original beaker. Since 100% is equivalent to the whole, we can say that the height of the larger beaker is twice the height of the original beaker.
Height of the larger beaker = 5 inches * 2 = 10 inches.
Now, let's calculate the volume of the larger beaker.
The volume of a cylindrical beaker can be calculated using the formula:
Volume = π * (radius)^2 * height,
where π is a constant value (approximately 3.14), and the radius is half the diameter of the beaker.
Since the beakers are similar, their dimensions are proportional. Therefore, the ratio of height in the larger beaker to the original beaker is the same as the ratio of their radii.
Let's call the radius of the original beaker r.
Since the ratio of their heights is 2:1, the ratio of their radii is also 2:1. This means that the radius of the larger beaker will be twice the radius of the original beaker.
Radius of the larger beaker = 2 * r.
Now, let's substitute these values into the formula for volume:
Volume of the larger beaker = π * (2 * r)^2 * 10.
Simplifying the equation:
Volume of the larger beaker = π * 4 * r^2 * 10.
Since the volume of the original beaker is given as 63 cubic inches, we can equate the two volumes and solve for r:
63 = π * r^2 * 5.
Divide both sides of the equation by π * 5:
12.6 = r^2.
Taking the square root of both sides gives us:
r = √12.6 ≈ 3.55.
Now, substitute the value of r into the equation for the volume of the larger beaker:
Volume of the larger beaker = π * 4 * (3.55)^2 * 10.
Calculating the volume gives us:
Volume of the larger beaker ≈ 502 cubic inches.
Therefore, the volume of the larger beaker is approximately 502 cubic inches.