Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 321

Surface Area

Surface Area
If the surface area of solid shape is 4cm^2 what can we infer about the shape?
Not a sphere (pi would lead to decimals)?
Same for cones and cylinders?
Pyramid?
Or does 4cm^2 have a square ‘ring’ to it? Should we be thinking cube/cuboid?

Also, at GCSE level (UK), or at any level for that matter, does 'solid shape' refer to 'straightforward' solid shapes, as opposed to the 3d versions of compound shapes?

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Surface Area

Where did that question spring from.

If r = 0.546189584... then a sphere's surface area = 4, so you cannot rule that out.

A cuboid 1 by 1 by 0.5 has surface area 4.

A cube with side 0.816497.... has surface area 4.

There are loads of possible shapes so there's not a lot you can say for certain.  A sphere has minimal surface area so you can probably say at least 1 dimension will be over the r given above.  You can probably get an upper bound for the shapes dimensions and I think that's about it.

A solid shape could certainly be a compound shape.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Surface Area

Where did that question spring from.

If r = 0.546189584... then a sphere's surface area = 4, so you cannot rule that out.

A cuboid 1 by 1 by 0.5 has surface area 4.

A cube with side 0.816497.... has surface area 4.

There are loads of possible shapes so there's not a lot you can say for certain.  A sphere has minimal surface area so you can probably say at least 1 dimension will be over the r given above.  You can probably get an upper bound for the shapes dimensions and I think that's about it.

A solid shape could certainly be a compound shape.

Bob

Can this be a question with many possible answers? Some questions will say this: MANY DIFFERENT ANSWERS IS POSSIBLE.