Math and Arithmetic
Geometry

# How does a surface area of a solid vary with its volume?

Provided the shape remains similar, the surface varies as the 2/3 power of the volume. Or, to put it another way, the cube root of the volume varies directly as the square root of the surface area.

Or,

the square of the volume is in direct proportion to the cube of the area.

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## Related Questions

The surface area would depend on the thickness of the layer formed by pouring out the gallon of liquid. The outside surface of a gallon container can also vary substantially based on its shape. Gallons are units of volume, not area.

as density is equal to mass per unit volume. for any substance, volume does not remain same in its three(solid, liquid and gas) state. so density vary when volume changes for different states of a substance

Fluid friction will vary with speed and the area of contact when referring to air friction or drag. When referring to surface friction then only the area of contact will vary.

No the area is when you are dealing with a 2-dimensional figure. Surface area formulas vary depending on if the object is a rectangular prism, a pyramid, a cone, or a triangular prism. a.k.a. the object needs to be 3-D to have a surface area.

There is no such thing as solid weight. All matter on Earth has weight whether it is solid, liquid or gas. There is also no such thing as a solid quart. A quart is a measure of volume usually applied to liquids or granulated substances such as flour or sugar. The volume of solid objects is usually measured in cubic centimeters or cubic inches. The volume of a given solid object will vary inversely with its density. The denser it is, the smaller it will be.

That means that the surface area (measured in acres, in this case) can vary.

There really isn't a "why"; that's just how things are. The volume of any solid with a cross-section that does not vary with height is the area of the base multiplied by the height.

When ths happens then the temperature should vary also its volume may change as well.

The amount of buoyant force is equal to the weight of the displaced water. The VOLUME of the displaced water is equal to the part of the solid that is submerged - thus, the buoyant force is equal to this volume, times the density of the water.

It's called surface area. The formulae vary depending on the shape. For example, a cube with a width of w has six sides, each of which has an area of w2, so the surface area of a cube is 6 x w2.

Surface area of the roof times depth of snow gives volume of snow. Take a sample of snow and weight it to determine density (since the density of snow can vary quite a bit). Density times volume equals weight.

Surface area? That will vary considerably. The smallest surface area will be if the water is suspended weightless, in the shape of a sphere. It could be in a pan 1/16 of an inch deep. Specify the shape you are interested in.

Liquid is the state of matter that has a defined volume, but not a defined shape. As opposed to a solid which has defined shape and volume, or a gas which has neither a defined shape nor volume. So the short answer is yes, a liquid will keep its volume. However, in the real world the volume of a liquid will vary as temperature and atmospheric pressure conditions change before transitioning to either a solid or gaseous state.

Minerals are solid substances that occur naturally in rocks and in the crust of the Earth. The type of mineral can vary depending on the area.

Statistics vary depending on the source, but it is believed that the average human has around six hundred million alveoli, giving a total surface area of approximately 100m2

Exactly the same as for a non-floating object. Finding the volume of a shape does not vary, (i.e it's always something along the lines of height*width*depth, or area of base *height. "Table" or "surface" is irrelevant, since if it not a variable in the formula). This is true whether the object is floating or not.

There is no single equation. Some simple shapes have equations and these vary from one shape to another. For most shapes there are no equations.

There are different formulae for different shapes and these vary in complexity.

Fees vary. You need to call around in your area.Fees vary. You need to call around in your area.Fees vary. You need to call around in your area.Fees vary. You need to call around in your area.

The volume of a drop can vary depending on the liquid in question. Surface tension, the speed the drop is excreted and temperature will all subtly affect volume. However the average volume is usually 40 to 50 micro litres per drop.

There is no such thing as a rectangular container since a rectangle is a 2-dimensional concept whereas a container is 3-dimensional. It could be 12 cm x 12 cm x 13.1250 cm which has a surface area of 918 sq cm. or 1 cm x 1 cm x 1890 cm with a surface area of 7562 sq cm or 1 mm x 1 mm x 189 metres with a surface area of 75600.02 sq cm.

A Surface table is a strong table you work on in engineering and the material on the surface can vary.

Friction only changes with two variables, the coefficient of Friction, and the Weight of the object, normal to the surface. Friction is independent of Surface Area. So, if increased roughness of the surface causes a change in the Coefficient of Friction, THEN the force of friction will be changed.