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Q: Why a piece of expanded polystyrene feels much lighter the an equal volume of lead?

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The volume of a cone is exactly equal to one third the volume of a cylinder of equal height and radius. The volume of a cylinder is equal to πr2h, so the volume of a cone is πr2h/3

Expressed in expanded form, 4069 is equal to 4000 + 60 + 9.

Volume of a prism is equal to the cross-sectional area multiplied by the height.

Since it is a CYCLE, the overall volume change from minimum volume to maximum volume and back must sum to zero, thus the volume expanded must equal the volume compressed. Now, bear in mind that the Carnot Cycle consists of 4 steps:Reversible isothermal expansion of the gas at the "hot" temperature, T1 (isothermal heat addition or absorption).Isentropic (reversible adiabatic) expansion of the gas (isentropic work output).Reversible isothermal compression of the gas at the "cold" temperature, T2. (isothermal heat rejection)Isentropic compression of the gas (isentropic work input).Although when you graph the cycle on a PV diagram, it looks pretty similar, there is no requirement that the volume change in step 1 matches the volume change in step 3, nor that the volume change in step 2 match that in step 4.

NO. If you mix them in equal parts, that would give you 35 volume. To get 15 volume, mix equal parts of 10 and 20 volume.

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It's equal in volume of course, but the ice will be lighter.

humid air is lighter that an equal volume of dry air at the same temperature.

Under the same conditions of pressure and temperature, any volumeof hydrogen weighs less than an equal volume of helium.

Gallon is a measure of volume, equal to 3.785 liters.Gallon is a measure of volume, equal to 3.785 liters.Gallon is a measure of volume, equal to 3.785 liters.Gallon is a measure of volume, equal to 3.785 liters.

The volume of a cone is exactly equal to one third the volume of a cylinder of equal height and radius. The volume of a cylinder is equal to πr2h, so the volume of a cone is πr2h/3

Expressed in expanded form, 4069 is equal to 4000 + 60 + 9.

volume of water an object displaces is equal to the volume of the part of the object inside it

Simply because the volume of water displaced is not equal to the actual volume of the object. If an object is lighter than water, you have to find another method of determining its volume. ------------------------------------ alternatively you could use a very thin pin to push the object under the water. However, the volume of the submerged portion of the pin would need to be suvtracted from the volume of the object measured.

Volume of a prism is equal to the cross-sectional area multiplied by the height.

NO. If you mix them in equal parts, that would give you 35 volume. To get 15 volume, mix equal parts of 10 and 20 volume.

Since it is a CYCLE, the overall volume change from minimum volume to maximum volume and back must sum to zero, thus the volume expanded must equal the volume compressed. Now, bear in mind that the Carnot Cycle consists of 4 steps:Reversible isothermal expansion of the gas at the "hot" temperature, T1 (isothermal heat addition or absorption).Isentropic (reversible adiabatic) expansion of the gas (isentropic work output).Reversible isothermal compression of the gas at the "cold" temperature, T2. (isothermal heat rejection)Isentropic compression of the gas (isentropic work input).Although when you graph the cycle on a PV diagram, it looks pretty similar, there is no requirement that the volume change in step 1 matches the volume change in step 3, nor that the volume change in step 2 match that in step 4.

The water displaced by the body is equal to its volume.