Table of Contents
- 1 Do shapes with the same volume have the same surface area?
- 2 Do two prisms with the same volume have the same surface area?
- 3 Can volume equal surface area?
- 4 Can different shapes have the same volume?
- 5 What is the relationship between volume and surface area?
- 6 What is difference between surface and volume?
Do shapes with the same volume have the same surface area?
ALL other shapes of the same volume MUST have larger surface area, and ALL other shapes of the same surface area MUST have smaller volume. Take a sphere of silly putty and squish it around, and you can increase the surface area as much as you like without changing the volume at all.
Do two prisms with the same volume have the same surface area?
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.
Do spheres with the same volume have the same surface area?
Area = 4 × π × r2 square units. So, your question really has no meaning: By choosing units appropriately, every sphere will have the same numerical value for its volume and surface area!
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.
Can volume equal surface area?
This is true for cubes, spheres, or any other object whose size is increased without changing its shape. The star on the line (at l = 6) represents the same point mentioned above: this is the size of the cube where S and V have equal values, and so the surface area to volume ratio is equal to one.
Can different shapes have the same volume?
And there you have it: two different shapes having the same volume. Volume is about the amount of space the shape occupies. As any measurement, different objects can have the same measurement – the same way two different people can have the same height.
Can volume and surface area be equal?
The star on the line (at l = 6) represents the same point mentioned above: this is the size of the cube where S and V have equal values, and so the surface area to volume ratio is equal to one.
Can two cylinders have different volumes but the same surface area?
Two figures can have the same volume but different surface areas. For example: A rectangular prism with side lengths of 1 cm, 2 cm, and 2 cm has a volume of 4 cu cm and a surface area of 16 sq cm.
What is the relationship between volume and surface area?
The volume is how much space is inside the shape. The surface-area-to-volume ratio tells you how much surface area there is per unit of volume. This ratio can be noted as SA:V. To find this ratio, you divide the formula for surface area by the formula for volume and then you simplify.
What is difference between surface and volume?
The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.