Can You Calculate Volume with Only the Radius and Not the Height?

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Calculating the volume of beans requires both the radius and height, as the formula V = πr²h indicates. With a diameter of 15.5 cm, the radius is 7.75 cm, but without the height, the volume cannot be determined directly. A suggested method to estimate volume is to use a measuring cup filled with water, noting the change in volume when the beans are submerged. Alternatively, finding a way to measure the height of the beans could also provide the necessary information. Accurate volume calculation is essential for proper measurement in experiments.
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I have a problem. I have to find the Volume of a group beans. Now I measured the bean's diameter, but I wasn't able to get Volume in the lab. Is there a way to get it?



The equation to find volume is V = (pi)r^2h... (pi times r squared, times H).
Volume of a solid is cm^3.




There are two variables missing, V and h. Now the diameter I have is 15.5cm... so the radius is 7.75cm.

So I have V = 3.14 * 7.75^2 * h

Is it possible to find the other two varibles?
 
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I know it might sound really dumb but if you've got a decently large and decently measured measuring cup fill it about half full with water and plop it in there and find the change in volume and convert it to cubic centimeters. Other then that find some other way to measure the height?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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