Hemispherical bowl Volume question

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In summary, the conversation is about a hemispherical bowl with a diameter of 60cm that is filled with punch to within 5cm of the top. After 30 minutes, there are only 5cm of punch left at the bottom of the bowl. The two questions asked are: a) how much punch was there at the beginning of the party? and b) how much punch was consumed? To find the answers, the volume of the hemispherical bowl is calculated using the formula V = 2/3(pi)(r)^3 and r = 30. By using h = 25 (since it is 30-5), a volume by revolution is done by shading the cross section of the part that was
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lovemake1
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Homework Statement



Question Reads...
A hemispherical bowl 60cm in diameter is filled to within 5 cm of the top. Thirty minutes after the party starts, there are only 5cm of punch left at the bottom of th bowl.

a) how much punch was there at the beginning of the party?
b) How much punch was consumed

Homework Equations



V of hemispherical bowl = 2/3(pi)(r)^3
r = 30
h = 30

The Attempt at a Solution



since this is a hemisphere we would have to find a volume using r interms of h right?
and by using h = 25 since its 30-5.

How should i begin? any advice appreciated.
 
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  • #2
I would draw a semicircle, shading the cross section of the part that was used and do a volume by revolution.
 

1. What is the formula for calculating the volume of a hemispherical bowl?

The formula for calculating the volume of a hemispherical bowl is V = (2/3)πr3, where V is the volume and r is the radius of the bowl.

2. Can the volume of a hemispherical bowl be directly measured?

Yes, the volume of a hemispherical bowl can be directly measured by filling it with a known quantity of water and then measuring the amount of water it holds. This method is known as the water displacement method.

3. How do you convert the volume of a hemispherical bowl from cubic units to other units?

To convert the volume of a hemispherical bowl from cubic units to other units, you can use conversion factors. For example, to convert from cubic inches to cubic feet, you would multiply the volume in cubic inches by 0.0005787.

4. Is the volume of a hemispherical bowl affected by the thickness of the bowl's material?

Yes, the volume of a hemispherical bowl is affected by the thickness of the bowl's material. The thicker the material, the smaller the volume will be due to the space taken up by the material itself.

5. How can the volume of a hemispherical bowl be used in real-life applications?

The volume of a hemispherical bowl can be used in real-life applications in various fields such as engineering, architecture, and cooking. It can be used to calculate the capacity of a storage tank, design a dome structure, or determine the amount of food that can fit in a bowl.

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