Can two objects have the same surface area but different volumes?

Can two objects have the same surface area but different volumes?

Surface area is a two-dimensional measure, while volume is a three-dimensional measure. Two figures can have the same volume but different surface areas.

Do all boxes with the same surface area have the same volume?

The geometric figure with the smallest surface-area/volume ratio is a sphere. Of the rectangular solids, it would be a cube. The closer a rectangular prism is to a cube, the smaller this ratio and conversely. Thus, having the same volume does not equal having the same surface area.

How does surface area vary with volume?

The increase in volume is always greater than the increase in surface area. For cubes smaller than this, surface area is greater relative to volume than it is in larger cubes (where volume is greater relative to surface area).

Do two cylinders with the same surface area have the same volume?

Do they have the same volume? Yes, due to Cavalieri’s principle. Even though these two cylinders are different, because they have the same height and base (and because every parallel cross section is congruent to the base), their volumes will be the same. The “slanted” cylinder is called an oblique cylinder.

How does volume and surface area relate to 2 dimensional area?

There is no definite relation between area and volume, as area is two dimensional and volume is 3 dimensional.

Is surface area always the same?

As we learned, the total amount of space inside an object is called its volume, while the total area of the surface of an object is called its surface area. However, the volume of the object always changes more than the surface area for the same change in dimensions.

Does a prism with more volume always have more surface area?

Surface area and volume can be easily calculated for simple geometric shapes like spheres, cylinders, and rectangular prisms. However, the volume of the object always changes more than the surface area for the same change in dimensions.

Why do smaller objects have a larger surface area to volume ratio?

Bigger the particle more of its mass contributes to its volume rather than its surface area but smaller the particle more of its surface area will be occupied by its mass than volume.

How does area and surface area relate?

The area is the measurement of the size of flat-surface in a plane (two-dimensional), whereas surface area is the measurement of the exposed surface of a solid shape (three-dimensional). This is the key difference between area and surface area. The unit for both the quantities is the same, though, i.e. square units.

What is the changing relationship between volume and surface area as an object gets bigger?

As the cube size increases or the cell gets bigger , then the surface area to volume ratio – SA:V ratio decreases. When an object/cell is very small, it has a large surface area to volume ratio, while a large object/ cell has a small surface area to volume ratio.

Why do smaller things have larger surface areas?

The smallest ball has little internal content (volume) compared to it’s outside surface area. Therefore it has a big surface area compared to it’s volume, so a high SA:Vol.

Do larger objects have a greater surface area?

This gives them a large ratio of surface to volume. Larger objects have small surface area compared to the volume so they have a small surface area to volume ratio. This shows how much surface area is required for each unit of volume.

Can two figures have the same surface area but different volumes?

A rectangular prism with side lengths of 1 cm, 1 cm, and 4 cm has the same volume but a surface area of 18 sq cm. Similarly, two figures can have the same surface area but different volumes.

What is the difference between sursurface area and volume?

Surface area and volume are calculated for any three-dimensional geometrical shape. The surface area of any given object is the area covered or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.

Why are the volumes of these two shapes the same?

The volumes of both shapes are the same, because volume measures the number of unit cubes that can be packed into a figure. Both shapes are built using the same number of cubes. Building shapes with different volumes would mean using fewer or more cubes. Shapes with the same volume like these two can have different surface areas.

Can two prisms have the same surface area but different volumes?

The volumes of the prisms are all different, but the surface areas are the same. Shapes with different volumes can have the same surface area. Volume is described in terms of unit cubes and surface area in terms of the exposed faces of those unit cubes. Can you find more examples of prisms that have the same surface areas but different volumes?