Question

This square pyramid has a surface area of 16 m2.

A square pyramid. The square base has side lengths of 2 meters. The triangular sides have a height of 3 meters.

Consider the square pyramid shown. If each dimension is doubled, how does the surface area change?
The surface area doubles.
The surface area triples.
The surface area increases by 4 times.
The surface area increases by 8 times.

Answer 1

If each dimension is doubled, the surface area changes by increasing four times (Option C)

What is a square pyramid?

A square pyramid is a pyramid whose base is in the shape of a square. Its volume is given as:

V = a³ (h/3);

The surface area is given as;

A = a² + 2a √((a²/4) + h))

Where:

a = base edge

h = height

If each dimension is doubled, how does the surface area change?

Recall the surface area equation above:

A = a² + 2a √((a²/4) + h))

if we input the original dimensions, we have:

2² + 2(2) * √((2²/4) + 3²)

= 16.65

If each dimension is doubled, then we have:

4² + 2(4) * √((4²/4) + 6²)

= 66.60

This means that the dimensions increased by 66.60/16.65

= 4

Hence the correct answer is option C.

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