Comparing Surface Areas of Two Water Balloons Using a Formula

In summary, the conversation discusses using a formula to compare the surface areas of two water balloons that have different volumes. The formula given is ((4pi)^(1/3))((3v)^(2/3)), where v represents the volume. By plugging in the volume of the first balloon (twice the volume of the second balloon) into the formula and simplifying, it is found that the first balloon will have about 1.59 times the surface area of the second balloon. The person confirms that it worked and thanks the other for their help.
  • #1
darshanpatel
139
0

Homework Statement



The question wants me to use this formula: ((4pi)^(1/3))((3v)^(2/3))

You have filled two round water balloons with water. One balloon contains twice as much water as the other balloon.

Compare the surface areas of the two water balloons using the given formula.

Homework Equations



None

The Attempt at a Solution



I don't know where to start
And I Don't Know where they got the answer from.

The book gave me a final answer as: The balloon with twice as much water will have about 1.59 times the surface area of the balloon with less water.
 
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  • #2
Say the volume of the other balloon is x. The volume of the first balloon is twice the volume of the other balloon, so that's 2x. Plug in x into the formula above and simplify. Then do the same for 2x. Compare the two expressions.
 
  • #3
ok, will try and let you know
 
  • #4
Yes, it worked, I got about 1.59, thank you
 

1. How do you calculate the surface area of a sphere?

The formula for the surface area of a sphere is 4πr², where r is the radius of the sphere.

2. Why is the surface area of a sphere important in science?

The surface area of a sphere is important in science because it is used to calculate various properties of objects such as volume, heat flow, and diffusion. It is also used in fields such as physics, chemistry, and biology to understand the behavior of particles and molecules.

3. What is the difference between surface area and volume of a sphere?

The surface area of a sphere is the measure of the total area that covers the outside of the sphere, while the volume is the measure of the space that is enclosed by the sphere. The surface area is a two-dimensional measurement, while the volume is a three-dimensional measurement.

4. Can the surface area of a sphere be negative?

No, the surface area of a sphere cannot be negative. It is a physical quantity that represents the amount of space that is covered by the surface of the sphere and therefore cannot have a negative value.

5. How is the surface area of a sphere related to other geometric shapes?

The surface area of a sphere is related to other geometric shapes such as a cube, cylinder, and cone, through their respective formulas. For example, the surface area of a sphere is equal to the surface area of a cylinder with the same radius and height, but it is half the surface area of a cube with the same edge length.

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